# Physics

The following modules are available to incoming Study Abroad students interested in Physics.

## PHYS101: The Physical Universe

• Terms Taught: Michaelmas Term only
• US Credits: 2 Semester Credits
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: college mathematics and physics

### Course Description

In this module you will have the opportunity to explore the nature and methods of physics by considering the different scales of the universe and the areas of physics which relate to them. You will model real phenomena and situations, looking at the physical principles which are fundamental to mechanics, particularly Newton's laws relating to forces and motion, and the principles of the conservation of energy and momentum. Later on you will also focus on the Special Theory of Relativity, beginning with Einstein's postulates and moving on to inertial reference frames, the physics of simultaneity, length contraction and time dilation, and space-time diagrams.

### Educational Aims

• To give a road map of the Part I Physics course and introduce the scales and dimensions of the classical and quantum worlds.
• To give a basic understanding of the physical principles which are fundamental to mechanics. The classical laws of Newton relating to forces and motion are discussed.
• To give an understanding of the origin of conservation laws.

### Outline Syllabus

• The nature of physics. Experiment and uncertainty. Modelling. Deterministic vs. probabilistic.
•  The universe ascending in scale, planets, stars, the Sun, galaxies, the expanding universe,  classical physics/mechanics. Forces: gravitation, electromagnetism.
•  The universe descending in scale, atoms, condensed matter, nuclei, particles. Links with cosmology.
• Quantum physics/mechanics.
•  Forces: electromagnetism, strong nuclear, weak nuclear.
• Relativity. Frames of reference.
•  Kinematics. Position, displacement, velocity and acceleration vectors. Motion in a straight line with constant acceleration. Motion in 2 dimensions. Projectile, circular motion.
• Dynamics. Newton's laws. Concepts of force and energy. Relations between force, momentum, energy, power. Kinetic and potential energy. Conservation of energy and momentum. Collisions, impulse.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS102: Classical Mechanics

• Terms Taught: Michaelmas Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits
• Pre-requisites: College mathematics and PHYS 101 or equivalent.

### Course Description

In Classical Mechanics you will apply the ideas of fundamental Newtonian mechanics to real large-scale systems such as rotating bodies, planetary systems and classical fluids. Our focus is on gravitation, and its central importance in determining the large-scale behaviour of the Universe. You'll look at concepts such as inertial and gravitational mass, Mach's principle, black holes and even dark matter.  We consider how to extend the principles of basic kinematics and dynamics to rotational situations, giving you an understanding of concepts of torque, moment of inertia, centre of mass, angular momentum and equilibrium. Part of your time will also be spent looking at how to describe basic processes in the properties of materials including elasticity of solids and fluid dynamics.

### Educational Aims

• To apply the ideas of fundamental Newtonian mechanics to real large scale systems such as rotating bodies, planetary systems and classical fluids.

### Outline Syllabus

• Relation between force, work and potential energy.
• Rotation of rigid bodies. Dynamics of rotational motion. Torque. Energy of rotation.
• Moment of inertia. Centre of mass. Angular momentum. Gyroscopes.
• Equilibrium. Properties of solids. Elasticity.
• The gravitational force. Inertial and gravitational mass. Mach's principle.
• Use of gravitational potential energy. Escape speed. Spherical mass distributions. Black holes. Dark matter.
• Motion of satellites and planetary orbits.
• Properties of fluids. Fluid dynamics. Viscosity.

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS103: Electric and Magnetic Fields

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College mathematics and PHYS 101 and 102 or equivalent.

### Course Description

Covering the basic laws of electromagnetism, this module allows you to investigate the similarities and differences between electric and magnetic fields, and to explore the basic concepts of electromagnetic phenomena including charge, current, field, force and potential. You'll begin by studying electrostatics, describing forces and fields due to charge distributions using Coulomb's law and Gauss's law. You'll also look at the concept of polarisation, and how this can be applied to capacitance and combinations of capacitors. Later on you will be introduced to magnetostatics, and will learn how to describe it using the concepts of field, flux and force, and the motion of charged particles in a magnetic field. You will also look at the origins of magnetic fields, Ampere's law, and Faraday's law of electromagnetic induction.

### Educational Aims

• To describe the basic laws and ideas of electromagnetism, starting with electrostatics.
• To introduce the ideas of force and potential, already experienced in PHYS 101 and PHYS102 in the context of electromagnetism.
• To stress the similarities and differences between electric and magnetic fields.

### Outline Syllabus

• Electric charge. Coulomb's law. Electric fields, field lines and forces. Electric dipoles. Electric flux. Gauss's law.
• Electric potential and potential energy. Potential difference and gradient. Capacitance. Series and parallel.
• Energy storage.
• Dielectrics. Polarisation.
• Magnetic field, flux, and force. Motion of charged particles in a magnetic field. Force on a current-carrying conductor. Magnetic dipole/current loop, force and torque.
•  Origin of magnetic fields. Field due to a (uniformly)moving charge. Force between parallel wires carrying current. Ampere's law and applications.
•  Electromagnetic induction. Faraday's law, Lenz's law. Motional EMF. Induced fields. Eddy currents.

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS104: Thermal Properties of Matter

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College mathematics and PHYS 101 and 102 or equivalent

### Course Description

This module allows you to study the thermal properties of matter, and to gain an understanding of how to relate them to the fundamental mechanical properties of systems. We begin with an introduction to the concepts of temperature and heat, thermal equilibrium and temperature scales. We then look at how to describe mechanisms of heat transfer, particularly in phase changes and equations of state, and the kinetic model of an ideal gas. As part of the module you will explore the first and second laws of thermodynamics, including concepts of internal energy, heat and work done, heat engines and refrigerators, and entropy. You will then learn about the role of thermodynamics in describing macroscopic physical situations, looking in particular at temperature, entropy, work, heat, and internal energy.

### Educational Aims

• To describe the thermal properties of matter and relate these to the fundamental mechanical properties of these systems.

### Outline Syllabus

• Temperature and heat. Thermal equilibrium. Zeroth law of thermodynamics. Thermal expansion.
• Temperature scales. Mechanisms of heat transfer. Phase changes. Black body radiation. Stefan-Boltzmann  law.
• Equations of state. Kinetic model of an ideal gas. Molecular speeds. Equipartition of energy.
• First law of thermodynamics. Work done. Different types of thermodynamic process, Thermodynamic states.
• Internal energy.
• Thermal capacity. Especially of an ideal gas.
•  Second law of thermodynamics. Heat engines. Refrigerators. Carnot cycle. Kelvin temperature scale.
• Entropy. Microscopic interpretation.

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS105: Quantum Physics

• Terms Taught: Summer Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.

### Course Description

The ultimate description of the universe requires quantum and not classical mechanics. In this module, we begin by investigating how specific experiments led to the breakdown of classical physics, before moving into the quantum world. You will look at the basic ideas of wave mechanics, particularly wave particle duality, as well as considering the probabilistic nature of phenomena and the uncertainty principle through the Schrodinger equation and its solution for simple situations.

### Educational Aims

The module aims to describe the quantum world, introducing the uncertainty principle and the probabilistic description furnished by quantum mechanics.

### Outline Syllabus

• Photoelectric effect. Work function. Energy of a photon. Franck-Hertz experiment. Spectra. Emission and absorption. The hydrogen spectrum.
• The nuclear atom. Rutherford scattering experiment. Bohr model of the atom. Discrete energy levels. Stable orbits.
• Wave particle duality. De Broglie waves. Electron diffraction. Single slit diffraction. Probabilistic interpretation.
• Uncertainty principle. Wave function and interpretation.
• The Schrodinger equation and pseudo-derivation from classical mechanics. Particles in a box. Potential wells. Tunnelling.

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS111: Functions and differentiation

• Terms Taught: Michaelmas Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College mathematics and physics.

### Course Description

Mathematical functions are used to describe physical phenomena and their graphical representation. This module is ideal for students wanting to gain a sound understanding of algebra, vectors and differentiation, and provides the tools needed for solving elementary equations involved in mathematical modelling, while strengthening problem-solving skills. During the course, you'll consider the fundamental principle of differentiation, and its relation to the slope of a graph. You will also learn how to differentiate basic functions directly, and how to use systematic techniques for combinations of functions.

### Educational Aims

This module aims to:

• provide a sound basis knowledge of algebra and vectors.
• give a sound understanding of differentiation and to apply these to modelling physical systems.

### Outline Syllabus

• Symbolic manipulation. Distinction between arithmetic of numbers and algebra of symbols.
• Symbols representing real numbers, their powers and inequalities.
• Cartesian coordinates, real valued functions and their graphs in 2D and 3D
• Angular measures (radians and degrees) and 2D and 3D polar coordinates.
• Periodic functions. Trigonometric functions.
• Inverse functions.
• Graphical location of real roots of quadratic and cubic equations
• Graphs of a xn for constant a > 0.
• Exponential function and notion of limits. Natural logarithm. Hyperbolic functions.
• Slope of a graph. The derivative of a real valued function of one variable.
• Rates of change and derivative of xn.
• Derivatives of sums and multiplication by constants
• Derivatives of exponentials, logs and trig functions
• Higher order derivatives
• Product and chain rule
• Logarithmic, parametric and implicit differentiation
• Determination of extrema of graphs and curve sketching. Extraction of small changes.

Workshops:

• The module includes a 1 hour workshop each week, run by the lecturer and postgraduate teaching assistants, as an extra learning aid, to develop problem solving skills, and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS112: Integration

• Terms Taught: Michaelmas Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: PHYS 111 or equivalent.

### Course Description

This module is ideal for students looking for a firm grounding in integration techniques. The module opens with an exploration of the fundamental principle of single-variable integration and it's relation to the area under a graph. This allows us to directly integrate a variety of basic functions of one variable. You will then consider systematic techniques to tackle more complicated integrals of one variable including integration by parts and by substitution. Finally you will study the important basic integrals over lines, areas and volumes.

### Educational Aims

To provide a firm grounding in integration techniques.

### Outline Syllabus

• Geometric area under a graph. The relation between anti-derivatives and the signed area generated by a graph
• Limit of a sum represented by a definite integral
• Definite integrals and area
• Indefinite and improper integrals
• Systematic techniques for integration
• Integration by parts
• Integration by substitution (change of integration variable)
• Simplification
• Integrals over lines
• Parametric evaluation of integrals over lines
• Introduction to integration over areas and volumes

Workshops:

The module includes a 1 hour workshop each week, run by the lecturer and postgraduate teaching assistants, as an extra learning aid, to develop problem solving skills, and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS113: Series and Differential Equations

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: PHYS 111 and 112 or equivalent

### Course Description

This module develops knowledge of series and functions as well as introducing ordinary differential equations and methods of solving them. You will first gain a good grounding in series and their formal representation, including geometric series, binomial expansion and the Taylor expansion. You'll then learn to describe the representation of functions by series, using trigonometric and exponential functions. In the second part of the module you will explore differential equations and their role in physics, including separable first order differential equations, second order differential equations for conservative systems and the method of integrating multiplier. As part of this you will also look at physical examples such as driven systems, harmonic force and the phenomenon of resonance.

### Educational Aims

• To develop a knowledge of series and functions
• To introduce ordinary differential equations (first and second order) and train in methods of their solution

### Outline Syllabus

• Series and their formal representation, summation sign. Convergence of infinite sums. Geometric series and summation of infinite geometric series. Binomial expansion and binomial coefficients Taylor expansion and Taylor polynomials. Series representations of trigonometric and exponential functions.
• Differential equations and their role in physics. Separable first order differential equations. Second order  differential equations for conservative systems and the method of integrating multiplier. Example of a harmonic oscillator problem.
• Linear ordinary differential equations. General and particular solutions of ODE. Properties of the function exp(Dx). The method of auxiliary equation for solving homogeneous ODE's. ODE's describing driven systems, harmonic force and the phenomenon of resonance.
• Based on FLAP modules

Workshops:

The module includes a 1 hour workshop each week, run by the lecturer and postgraduate teaching assistants, as an extra learning aid, to develop problem solving skills, and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS114: Complex methods

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: PHYS 113 or equivalent.

### Course Description

This module provides an introduction to the concept of complex numbers and how they relate to applications in modelling physical ideas. You will begin by investigating the principle of complex representation, looking at real and imaginary numbers, complex conjugation, Argand diagrams and different representations of complex numbers, such as Cartesian, polar, and exponential. You will then develop skills in the manipulation of complex functions and the determination of the complex roots of equations. You'll also consider physical applications, such as the use of complex methods in AC circuit analysis, the complex representation of harmonic waves, and the solution of differential equations describing damped oscillatory motion.

### Educational Aims

On completion of the module, students should be able to:

• understand the principle of complex representation
• manipulate complex functions and to obtain complex roots to equations
• recognise the mathematical simplification resulting from the use of the technique to describe phenomena involving phase and amplitude
• apply their knowledge to modelling real phenomena and situations

### Outline Syllabus

The course will cover:

• imaginary numbers
• real and imaginary parts, complex conjugate and modulus of a complex number
• simplification and rationalisation
• Fundamental Theorem of Algebra and roots of real polynomial equations
• complex arithmetic
• Argand diagram
• complex numbers in polar form
• representation on the complex plane and the argument (phase) of a complex number
• principal value
• exponential form and Euler's formula
• use in operations on complex numbers, including roots, reciprocals, real and complex powers
• De Moivre's Theorem
• trigonometric identities
• roots of unity
• complex algebra
• factorizing and simplifying functions
• relation between trigonometric and hyperbolic functions and complex exponentials
• functions of a complex variable
• differentiation of complex functions
• conformal mapping
• use of complex methods in AC circuit analysis
• complex representation of harmonic waves
• solution of ODE describing 1D damped oscillatory motion using complex methods
• related application

Workshops:

The module includes a 1 hour workshop each week, run by the lecturer and postgraduate teaching assistants, as an extra learning aid, to develop problem solving skills, and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS115: Vector Calculus

• Terms Taught: Summer Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: PHYS 114 or equivalent.

### Course Description

This module is ideal for students looking to develop their understanding of vector algebra and coordinate geometry in a physical context, extending elementary ideas of functions and calculus to a three-dimensional description based on vector fields and potentials. You will begin by exploring the real functions of many variables and their partial derivatives, followed by implicit differentiation of the functions of many variables and the chain rule. You will then go on to study the gradient vector in three dimensions in relation to directional derivatives, and will investigate the divergence and curl of a vector field as well as Stokes' theorem and the divergence theorem. Vector Calculus places a focus on calculus in higher dimensional space, allowing you to develop your knowledge of parametric representations of curves, surfaces and volumes, calculation of areas and volumes including the use of changes of variables and Jacobeans, and the calculation of line and surface integrals.

### Educational Aims

To develop a firm grounding in vector algebra and coordinate geometry in a physical context.

### Outline Syllabus

• Real functions of many variables, and their partial derivatives.
• Implicit differentiation of functions of many variables and the chain rule.
• Scalar and vector fields in 3D. Gradient vector in 3D. Normal vector to a surface in 3D and its tangent plane.
• Directional derivatives in terms of the gradient field. Perfect differentials and relation to potentials for force fields.
• Parametric representation of curves, surfaces and volumes in space. Calculation of areas and volumes.
• Change of variables and the Jacobian determinant. Spherical and polar cylindrical coordinates.
• Line and surface integrals and their applications.
• Divergence of a vector field and Gauss theorem. Curl of a vector field and Stokes theorem.
• The local and global description of electromagnetic phenomena in terms of vector fields, div, grad and curl.

Workshops:

The module includes a 1 hour workshop each week, run by the lecturer and postgraduate teaching assistants, as an extra learning aid, to develop problem solving skills, and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 40%
• Exam: 60%

## PHYS131: Vectors & Vector Algebra / IT Skills

• Terms Taught: Michaelmas Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College Mathematics and Physics.

### Course Description

This module will introduce you to the methodology of vectors and vector algebra, including their application to three-dimensional motion, during a series of lectures and practical sessions. You will learn to recognise the orthogonality of the dimensions of space and use vectors to describe them; demonstrate a facility with the techniques of vector algebra, including the use of vector products; and be able to apply this knowledge to modelling real phenomena and situations. The practical element of the course sees you working in one of our PC labs learning how to best utilise spreadsheets and symbolic computations, and how to present data.

### Educational Aims

On completion of the module, students should be able to:

• recognise the orthogonality of the dimensions of space and the use of vectors to describe them
• demonstrate a facility with the techniques of vector algebra, including use of vector products
• apply this knowledge to modelling real phenomena and situations
• operate common PC based word processors, spreadsheets and Internet browsers
• prepare word processed reports

### Outline Syllabus

Lecture component:

• Distinction between scalars and vectors.
• Real displacement vectors in 3D and their addition and multiplication by scalars.
• Linear independence between sets of vectors.
• Notion of a basis.
• Distinction between vectors and their components in different bases.
• The standard basis i, j, k Scalar product of two vectors and the angle between two vectors.
• Rotation of axes in 2D.
• Vector product of two vectors.
• Vector moment of a force about a point.
• Vector forces and the equilibrium of a particle under the action of several forces.
• Motion of a particle in terms of a time-dependent vector.
• Velocity and acceleration vectors.
• Motion in polar coordinates.
• Centrifugal and Coriolis acceleration.
• Scalar-triple product and volume of a parallelepiped.
• Moment of a force about an axis of rotation.
• Vector-triple product.
• Definition of a rigid body and vector angular velocity.

Practical component:

An introduction to the PC:

• Internet exploration,
• Word processing, including the insertion of tables and graphics into the document, with MS Word and LaTeX.
• Spreadsheets as an iterative calculation tools for physics problems, work with Excel, Origin and Maple programs.
• computer graphical presentation of data,
• symbolic computations.
• Report writing using Internet search and all software tools considered in this module.

### Assessment Proportions

• Coursework: 70%
• Exam: 30%

## PHYS132: Basic Physics Skills / Communication Skills

• Terms Taught: Michaelmas Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College Mathematics and Physics.

### Course Description

This module is made up of both lectures and practical sessions, aiming to developing your communication skills through the preparation and delivery of a verbal presentation and written scientific report. The lectures will allow you to consider systematic approaches to problem solving including good methods in working and presenting answers, and in selecting and testing maths expressions in modelling. You will also develop a theoretical understanding of the basic principles of measurement and record-keeping, and will look at the best methods for assessing the significance of experimental data through consideration of uncertainties and statistical analysis. The practical sessions develop your skills and awareness for implementing informed career decisions. You will explore the need for ethical behaviour, both in the context of an undergraduate physics degree and scientific research in general.

### Educational Aims

Lecture component:

• To introduce problem solving techniques. To teach the theoretical basis of data recording and analysis

Practical component:

• To introduce the methodology of experimental measurement.

### Outline Syllabus

Problem Solving:

• Systematic approach via preparing, planning, working, checking good methods in working and presenting answers;
• exam question code words selecting and testing maths expressions in modelling.

Data Analysis:

• systematic, instrumental and random uncertainties;
• finding values for the mean, median and standard deviation;
• uncertainty in the mean;
• combining uncertainties in sum/difference and addition/division cases;
• significance of uncertainty in results.
• uncertainty in counts and count rates;
• uncertainty in graph drawing;
• uncertainty in functions;
• the effect of variously weighting data.
• distribution functions (binomial, Poisson and normal Gaussian).
• noise and its sources.
• linear regression;
• correlation and its use to find uncertainty in gradients;
• the Chi squared test.
• keeping a good laboratory log book.

Practical component:

• Communication skills
• Oral presentation
• Structure of a formal scientific report
• Preparation of OHP slides and poster (group work)

### Assessment Proportions

• Coursework: 70%
• Exam: 30%

## PHYS133: Oscillations & Waves / Practical Lab I

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: PHYS 102 and 112 or equivalent.

### Course Description

This exciting practical module on Oscillations and Waves allows you to investigate how wave and oscillatory phenomena arising in quite different areas of physics can be described in a very similar way, focusing in particular on the widely applicable model of simple harmonic motion.

You will then learn to recognise the wave equation and will develop the ability to solve it for a general situation, to calculate appropriate physical parameters describing a wave, and understand universal wave phenomena such as interference, beats and wave packets.

Part of this module is taught in the laboratory, giving you the opportunity to work with a wide range of measurement instrumentation. Through your practical work you ll also gain an appreciation for the importance of uncertainties in experimental measurements and how to apply them in an appropriate manner.

### Educational Aims

Lecture component:

On completion of the module, students should be able to:

• appreciate the wide applicability of the model of simple harmonic motion
• recognise the wave equation, and the ability to solve it for a general situation
• calculate appropriate physical parameters describing a wave
• understand the universal wave phenomena such as interference, beats, and wave packets.

Practical component:

On completion of the module, students should be able to:

• recognise a wide range of measurement instrumentation
• use and measure with common instrumentation
• appreciate the importance of uncertainties in experimental measurements and be able to apply them in an appropriate manner
• write coherent, structured reports based on their experiments

### Outline Syllabus

Lecture component:

• Periodic motion.
• Hooke's law.
• Simple harmonic motion.
• Simple pendulum. Physical pendulum.
• Driven and damped harmonic motion.
• Mathematical description of waves.
• Speed, polarisation, energy flow.
• Doppler effect.
• Waves in gases (sound).
• Waves in solids (elastic).
• Wave interference and normal modes.
• Standing waves.
• Resonance.
• Beats, wave packets.

Practical component:

• An introductory laboratory where a range of experiments is available which will allow the development of data taking, analysis and deductive reasoning skills.
• Familiarisation with different instruments and techniques will occur through the varied range of experiments.

### Assessment Proportions

• Coursework: 70%
• Exam: 30%

## PHYS134: Electrical Circuits & Instruments / Practical Lab II

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College Mathematics and PHYS 103 or equivalent.

### Course Description

This exciting module has practical emphasis. Through exploration of the effect of simple electrical components in DC and AC circuits you will build an understanding of the basic principles determining the behaviour of voltage and current in DC and AC circuits, and you'll learn to quantitatively analyse circuits containing resistance, capacitance and inductance. Working in the laboratory, you will gain practical experience of using instruments and experimental equipment, and develop your skills in making experimental measurements, recording and analysing data, and report writing.

### Educational Aims

Lecture component:

On completion of the module, students should be able to:

• understand the basic principles determining the behaviour of voltage and current in DC and AC circuits
• analyse quantitatively such circuits containing resistance, capacitance and inductance

Practical component:

On completion of the module, students should be able to:

• exhibit practical experience of using common instruments and experimental equipment,
• have developed skills of making experimental measurements, recording and analysing data and writing reports.

### Outline Syllabus

Lecture component:

• DC circuits
• Voltage current
• Potential difference
• EMF
• Resistance
• Ohm's law
• Kirchoff's laws
• Power dissipated
• DC Meters
• AC circuits
• Combinations of resistance
• Inductance and capacitance
• Phasors and trigonometry
• Impedance
• Transformers
• Motors and generators

Practical component:

• Experimental laboratory to illustrate physical principles described in lectures, and to develop skills of measurement and use of common instrumentation.
• A further range of experiments is available which will allow the development of data taking, analysis and deductive reasoning skills.
• Familiarisation with different instruments and techniques will occur through the varied range of experiments.

### Assessment Proportions

• Coursework: 30%
• Exam: 70%

## PHYS135: Optics & Optical Instruments / Practical Lab III

• Terms Taught: Summer Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: College Mathematics and PHYS 131 or equivalent.

### Course Description

In this module you'll be introduced to the principles of geometrical optics and will learn how to practically apply them to instruments and experimental equipment in a laboratory setting, giving you a practical reference for the physical principles discussed in your lectures. You will develop your understanding of commonly encountered optical phenomena, use geometrical optics to analyse optical systems, and understand the functions and basic principles of operation of some important optical instruments.

### Educational Aims

Lecture component:On completion of the module, students should be able to:

•  appreciate and explain commonly encountered optical phenomena,
•  display an ability to use the methods of geometrical optics to analyse optical systems,
•  understand the functions and basic principles of operation of some important optical instruments.

Practical component:On completion of the module, students should be able to:

• display a knowledge of instruments used in making optical measurements,
• exhibit practical experience of using common instruments and experimental equipment,
• have developed skills of making experimental measurements, recording and analysing data and writing reports.

### Outline Syllabus

Lecture component:

• The nature of light.
• Coherence.
• Reflection, refraction, dispersion, polarisation.
• Geometrical optics.
• Lenses and mirrors.
• Instruments.
• Microscope.
• Telescope.
• Camera.
• Resolving power.
• Aberrations.
• Basic principles and applications, especially telescopes.
• Optical fibres.
• Interference and diffraction.
• Michelson interferometer.
• Diffraction grating.

Practical component:

• Experimental laboratory to illustrate physical principles described in lectures, and to develop skills of measurement and use of common instrumentation.
• A final laboratory where a further range of experiments is available which will allow the development of data taking, analysis and deductive reasoning skills. Familiarisation with different instruments and techniques will occur through the varied range of experiments.

### Assessment Proportions

• Coursework: 30%
• Exam: 70%

## PHYS211: Maths I

• Terms Taught: Michaelmas Term only.
• US Credits: 4 Semester Credits.
• ECTS Credits: 8 ECTS Credits.
• Pre-requisites: PHYS 110, PHYS 131 or equivalent.

### Course Description

Designed to provide students with a working knowledge of the basic mathematical techniques that are required when studying physics at degree level and beyond, this modules range of topics include a look at linear algebra, where students will discover coupled linear equations, linear transformations and normal modes of coupled oscillators. A section on Hilbert space will address wave equation, bases of functions and Kronecker delta-symbol, and angular harmonics will be covered in detail. Over the duration of the module, students will become familiar with Pauli matrices, eigenvalues, eigenvectors and commutation relations, and will develop a range of skills and techniques required for solving various common types of linear equations. Additionally, a workshop led by postgraduate teaching assistants will be held every two weeks to provide extra one-to-one tuition and support with coursework assignments as required.

### Educational Aims

The module aims to provide a working knowledge and understanding of the basic mathematical techniques required for studying physics at degree level and beyond. In particular:

• to provide a basic working knowledge of linear algebra, transformations, matrices and matrix operations;
• to introduce Pauli matrices, eigenvalues, eigenvectors and commutation relations;
• to provide skills and techniques for solving various common types of linear equations.

### Outline Syllabus

• Linear algebra: Systems of coupled linear equations
• Linear transformations
• Determinant of a matrix
• Diagonalisation of matrices
• Pauli matrices and practicing in operations with them
• Eigenvalues and eigenvectors
• Symmetric and Hermitian matrices and their diagonalisation using orthogonal and unitary matrices
• Solving systems of linear ordinary differential equations, normal modes of coupled oscillators
• Commutation relations involving matrices, invariants of linear transformations
• Hilbert Space: Wave equation in 1D with boundary conditions, separation of variables using standing waves
• Wave equation in 3D: separation of variables and resonances in a drum
• Bases of functions
• Orthogonality of harmonic functions, Kronecker delta-symbol, and completeness of a basis
• Angular harmonics
• Operators and their eigenfunctions
• Angular harmonics in 2 dimensions, relation between plane waves and cylindrical waves, Bessel functions
• Laplace operator in Cartesian, cylindrical and spherical coordinates
• Spherical harmonic functions in 3 dimensions
• Representation of operators as matrices acting in the Hilbert space, commutation relations between operators

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS213: Maths II

• Terms Taught: Lent / Summer Terms only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 110, PHYS 211.

### Course Description

This module introduces the Fourier series and transforms, and addresses their application to examples in physics. Students will learn how to express a periodic function as a Fourier series, and find the Fourier transform of a function.  Additionally, students will solve linear ODEs and PDEs using Fourier techniques, as well as developing the ability to solve problems with initial conditions and/or spatial boundary conditions.

### Educational Aims

On completion of the module, students should be able to:

• express a periodic function as a Fourier series;
• find the Fourier transform of a function;
• solve linear ODEs and PDEs using Fourier techniques;
• solve the diffusion equation with initial conditions and/or spatial boundary conditions.
• process verbal information during a lecture and make appropriate notes;
• apply their physics and mathematical knowledge to solve problems.

### Outline Syllabus

Fourier series representation of periodic functions:

• Real and complex Fourier series
• Examples of Fourier expansion of periodic functions
• Application of Fourier series to physical systems with forced oscillations and dissipation, mechanical and electrical
• Parseval's theorem

Fourier transform:

• Expression of a function as a Fourier integral
• Definition of the Fourier transform and its inverse
• The integral representation of the Dirac delta-function
• General solution of the wave equation using Fourier transforms
• 1-D wave equation with initial conditions - d'Alembert's solution
• Convolution

Boundary and initial condition problems:

• The diffusion equation, derivation and time-dependent solution with initial conditions.
• The heat equation.
• Laplace's equation, the Uniqueness Theorem, arbitrary boundary conditions.
• Applications to electrostatics.

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS221: Electromagnetism

• Terms Taught: Michaelmas Term only.
• US Credits: 4 Semester Credits.
• ECTS Credits: 8 ECTS Credits.
• Pre-requisites: PHYS 100 and PHYS 110.

### Course Description

Students will receive an introduction to Maxwell's Equations, including Faraday's law, displacement current, Maxwell's equations in point and integral form and retarded potentials. The module explores Plane Waves, EM phenomena in polarisable and magnetisable media and plane waves at boundaries. Students will become familiar with transmission lines, along with wave guide and antennas. Students will be taught through a series of lectures to develop their understanding of the core material, and seminars will consolidate and assess their progress. Students will learn to appreciate the power of vector calculus and Maxwell's equations for the description of electromagnetic phenomena, and will eventually gain the skillset required to describe electromagnetic fields and waves created by various simple configurations of charges and currents, as well as gaining the necessary knowledge to understand the effects of media on the propagation of electromagnetic waves.

### Educational Aims

On completion of the module, students should be able:

• to display an understanding of Maxwell's equations, in various forms, for the description of electromagnetic phenomena;
• to appreciate and utilize the power of vector calculus to solve Maxwell's equations in some common physical problems;
• to describe electromagnetic fields and waves created by various simple configurations of charges and currents;
• to understand the effects of media on the propagation of electromagnetic waves.

### Outline Syllabus

• Vector and scalar fields.
• Gauss's law.
• Charge and current densities.
• Conductors and dielectrics, permittivity.
• Capacitance.
• Biot-Savart's law.
• Ampere's law.
• Vector potential.
• Magnetic forces, magnetization, permeability. Inductance.
• Multipole expansion.
• Electric and magnetic dipoles.
• Maxwell's equations in differential and integral forms.
• Maxwell's equations for potentials.
• Energy of electromagnetic field, Poynting theorem.
• Maxwell's equations in free space.
• Electromagnetic waves.
• Plane e/m waves.
• Propagation in free space and dielectrics.
• Propagation in conductors, skin depth.
• Boundary conditions.
• Plane waves at boundaries.
• Reflection and refraction, refractive index.
• Standing waves.
• Hertzian oscillator.
• Antennas.
• Wave guides.
• TE wave in a rectangular wave guide.
• Dielectric wave guides.
• Transmission Line Equations.
• Telegraph line, coaxial cable.

Workshops:

The module includes workshops, run primarily by postgraduate teaching assistants, as an extra learning aid and to help tackle coursework assignments.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS222: Electromagnetism, Waves and Optics

• Terms Taught: Michaelmas Term only.
• US Credits: 5 Semester Credits.
• ECTS Credits: 10 ECTS Credits.
• Pre-requisites: PHYS 100 and PHYS 110.

### Course Description

This module provides students with a working knowledge of electromagnetism through Maxwell's equations using the tools of vector calculus. Students will become familiar with the common connections between the many different phenomena in nature that share the mathematical model of a harmonic oscillator or of a wave. This module addresses the basic properties of wave propagation, diffraction and inference, and laser operation. Students will develop an appreciation for the power of vector calculus and Maxwell's equations for the description of electromagnetic phenomena, and will gain practical knowledge of Fresnel and Fraunhofer diffraction, as well as thin-film interference fringes and anti-reflection coatings. Additionally, the module aims to enhance students understanding of the origin of polarisation, and the relevance of dichroism, along with an understanding of the basic elements of a laser, laser operation and important features of laser light.

### Educational Aims

On successful completion of this module students will be able to:

• appreciate the power of vector calculus and Maxwell’s equations for the description of electromagnetic phenomena
• to describe electromagnetic fields and waves created by various simple configurations of charges and currents
• to understand the effects of media on the propagation of electromagnetic waves
• determine image position and magnification using the mirror equation or simple lens equation
• describe diffraction experiments using superposition of complex wavelets
• discuss thin-film interference fringes and anti-reflection coatings
• describe the diffraction grating and the dispersion of light
• discuss Fresnel and Fraunhofer diffraction
• discuss the origin of polarisation, and the relevance of dichroism
• describe the basic elements of a laser, laser operation and important features of laser light

### Outline Syllabus

Electromagnetism:

• Vector and scalar fields.
• Gauss's Law.
• Scalar potential and its gradient.
• Charge and current densities.
• Conductors and dielectrics.
• Polarisation, permittivity.
• Capacitance.
• Lorentz force, Biot-Savart law.
• Ampere's law.
• Vector potential.
• Magnetisation, permeability.
• Inductance.
• Multipole expansion.
• Electric and magnetic dipoles.
• Ohm's law, electromotive force.
• Maxwell's equations in differential and integral forms.
• Maxwell's equations for potentials.
• Energy of electromagnetic field, Poynting theorem.
• Gauge invariance.
• Maxwell's equations in free space.
• Electromagnetic waves.
• Plane e/m waves.
• Propagation in free space and dielectrics.
• Propagation in conductors, skin depth.
• Boundary conditions.
• Plane waves at boundaries.
• Reflection and refraction, refractive index.
• Standing waves.
• Wave guides, coaxial cable.

Waves and Optics:

• Fermat's Principle
• Revision of basic geometric optics
• Reflection and refraction
• Mirrors, lenses and prisms
• Summary of wave phenomena: electromagnetic spectrum, light, microwaves, sound, waves on strings and in solids: relation to oscillations
• The wave equation and its solution
• Basic concepts: amplitude, phase, normal modes, resonance,superposition, polarisation, dispersion relation, phase and group velocity
• Diffraction
• Huygens Principle
• Fraunhofer diffraction
• Single and multiple slit optical phenomena
• Diffraction grating
• Dispersion of light
• Circular aperture
• Rayleigh criterion
• Fresnel diffraction
• Interference and coherence
• Experiments: Fresnel's biprism, Lloyds mirror, thin films
• Polarisation
• Linearly and circularly polarised light
• Reflection and refraction at a plane interface
• Fresnel Equations
• Brewster's angle
• Rayleigh scattering
• Polarisation by scattering
• Polarisation by absorption (dichroism)
• Polarisation filters and Malus' law

Lasers:

• stimulated emission
• basic elements of a laser: medium, pumping and population inversion
• standing waves in optical cavities
• the important features of laser light such as coherence, monochromaticity and directionality
• examples of laser types

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS223: Quantum Mechanics

• Terms Taught: Lent / Summer Terms only.
• US Credits: 4 Semester Credits.
• ECTS Credits: 8 ECTS Credits.
• Pre-requisites: PHYS 100 and PHYS 110.

### Course Description

Students will be introduced to various axioms for quantum mechanics, such as eigenvalues, diagonalisation, differential and matrix operators and commutation relations. They will also learn about rotations and angular momentum, the interaction of magnetic moment with static magnetic field and electron spin. Students can expect to investigate approximation methods, such as the time-dependent Rayleigh-Schrodinger perturbation theory, and time dependent interactions, including the Heisenberg picture and time dependent Hamiltonians. Students will learn to apply quantum mechanics to problems in one and three dimensions, including the hydrogen atom, by solving the Schrodinger equation, and will develop the ability to find approximate solutions for not exactly solvable systems. The module will enhance students understanding of expectation values and probabilities in the context of experiments on quantum systems, along with an appreciation for the mathematical consistency of quantum mechanics.

### Educational Aims

On completion of the module, students should be able to:

• Apply quantum mechanics to simple, exactly solvable problems in one and three dimensions, including the hydrogen atom, by solving the Schrodinger equation;
• systematically find approximate solutions for systems that are not exactly solvable;
• work out predictions for expectation values and probabilities in the context of experiments on quantum systems;
• understand and appreciate the mathematical consistency of quantum mechanics.

### Outline Syllabus

Revision of essential mathematics for quantum mechanics:

• analysis of trigonometric and exponential functions
• ordinary and partial differential equations
• linear algebra with two-component vectors and matrices
• particle-wave duality and the Schrodinger equation

Applications in 1d:

• particle in the box
• piecewise constant potentials
• harmonic oscillator
• notions of bound state, ground state, zero-point energy, tunnelling and resonance
• stationary perturbation theory and the variation technique

Applications in 3D:

• 3D particle in the box
• 3D harmonic oscillator
• angular momentum
• hydrogen atom

Spins and electrons in magnetic fields:

• cyclotron motion
• Stern-Gerlach experiment
• spin precession
• Zeeman effect

Many particles (Pauli principle and chemical table of elements)

Axioms and advanced mathematics of quantum mechanics:

• states as vectors (superposition principle); associated linear algebra
• time dependence
• observables as operators; associated linear algebra and functional analysis (eigenvalue problems, Fourier analysis)
• probabilities and expectation values;
• commutation relations
• uncertainty principle
• comparison to classical mechanics

Dirac notation; compact revision of the module

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS232: Relativity, Nuclei and Particles

• Terms Taught: Michaelmas and Summer Terms only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 100 and PHYS 110.

### Course Description

Students receive an introductory concepts-based approach to the module, giving a basic understanding of nuclei and fundamental particles. The module covers the general properties of nuclei, such as composition, the forces within the nucleus, mass and binding energy. Students are then introduced to the standard model of particle physics, including the three generations of fundamental particles. By the end of the module, students will gain a working knowledge of Einstein's Theory of Special Relativity, both conceptually and mathematically, and will understand why the theory has replaced Newton's concepts of absolute space and time. Additionally, students will develop a broad understanding of the equivalence principle and its relevance for general relativity.

### Educational Aims

• To provide students with a working knowledge of Einstein's theory of Special Relativity, both conceptually and mathematically.
• To provide students with a qualitative understanding of the Equivalence Principle and its relevance for General Relativity.
• To give students a basic understanding of atomic nuclei and of fundamental particles and their interactions.
• To develop skill in processing verbal information during a lecture and making appropriate notes.
• To develop the ability to find additional information from a variety of sources including textbooks, scientific papers, the library and the internet.
• To develop the ability to look for patterns and similarities in various nuclear and particle interactions in order to unpack and simplify seemingly-complicated problems.
• To enhance problem-solving and mathematical skills by requiring students to apply their mathematical skills and physics understanding to a variety of problems in relativity.

### Outline Syllabus

PHYS232 covers the topics of Relativity (50%) and Nuclei and Particles (50%).

Relativity:

• Absolute space and time in Newtonian mechanics,
• implications of conservation laws,
• inertial frames,
• the Standard Configuration,
• Galilean Transformation,
• the Principle of Relativity,
• the Luminiferous Aether concept.
• the speed of light in relation to movement of source and observer,
• stellar aberration,
• the Michelson-Morley experiment,
• aether drag and viscosity experiments,
• Morley and Miller follow-up work, F
• FitzGerald-Lorentz contraction,
• the constancy of c.
• Special Relativity and time dilation,
• length contraction as a consequence,
• the example of muon decay,
• mass, energy and speed, E = mc2 and nuclear energy.
• loss of simultaneity but not causality.
• Proofs of Relativity.
• The Lorentz transformation,
• reciprocity in relativity,
• spacetime diagrams,
• Doppler effect (radial and transverse),
• transformation and addition of velocities,
• light intensity,
• "observing" and "seeing" at high speed.
• Relativistic momentum and energy,
• centre of mass frame.
• Relativistic electromagnetism.
• The light cone, past,future and elsewhere,
• space-time intervals,
• proper time,
• proper distance.
• Three-vectors and four-vectors,
• scalar products of four-vectors,
• the energy-momentum four-vector,
• relativistic acceleration and force.
• Four-momentum conservation,
• inelastic collisions and Compton scattering.
• Four-vectors in electromagnetism.
• General Relativity,
• the Principle of Equivalence,
• local inertial frames.
• Spacetime curvature,
• non-Euclidean geometry,
• a metric basis for gravity,
• field equations,
• Schwarzschild metric solution,
• Schwarzschild black hole,
• light speed in curved space,
• bending, slowing and lensing effects for light,
• gravitational redshift,
• binary pulsar.

Nuclei and Particles:

• This is an introductory, concepts-based course designed to give students some basic understanding of nuclei and of fundamental particles, i.e. particles with no observed substructure. The course covers the general properties of nuclei, such as composition, the forces within the nucleus, mass, binding energy, isotopes,isobars, and isotones. The Liquid Drop Model of nuclei and the Semi-Empirical Mass Formula are presented.
• Alpha, beta and gamma decays, fission and fusion, and nuclear reactions such as neutron activation, are discussed.
• Students are then introduced to the Standard Model of Particle Physics, including the three generations of fundamental particles; the strong, weak and electromagnetic fundamental forces; quark and lepton flavours;the composition of matter; conservation laws such as conservation of baryon number, lepton number or flavour; and the force propagators: photons, W and Z particles, and gluons. The Higgs particle, and factors that affect cross-sections and decay rates are discussed. Examples of measurements from recent and current experiments often are used to illustrate the concepts.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS233: Thermal Properties of Matter

• Terms Taught: Lent / Summer Terms only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 100 and PHYS 110.

### Course Description

This module provides a review of thermodynamic equilibrium, temperature, zeroth law, reversible and irreversible processes, as well as heat, work and internal energy. Students will be introduced to the Boltzmann distribution and apply the Boltzmann distribution to solids, paramagnetism, heat capacity, defects in solids.  The module offers students the opportunity to explore crystal structure and symmetry, lattices, symmetry operations and unit cells. Students will investigate the quantum mechanical free electron model and basic band structure ideas in nearly free electron and tight binding pictures as part of the module.

Students will develop an appreciation for the connections between the microscopic and macroscopic pictures of the thermal properties of solids, and will gain the skillset required to account for some fundamental properties of solids in statistical terms. Additionally, students will become familiar with the use of thermodynamic potentials and associated thermodynamic relations, and will gain an awareness of the different kinds of phase transition and how they are classified. Finally, students will gain the necessary knowledge required to understand the evidence for the third law of thermodynamics and how it relates to the unattainability of absolute zero.

### Educational Aims

On completion of the module, students should be able to:

• describe the connections between the microscopic and macroscopic pictures of the thermal properties of solids;
• account for some fundamental properties of solids in statistical terms.
• show a familiarity with the use of thermodynamic potentials and associated thermodynamic relations;
• display an awareness of the different kinds of phase transition and how they are classified;
• display an understanding of the evidence for the Third Law of Thermodynamics and how it relates to the unattainability of absolute zero.

### Outline Syllabus

• Review of thermodynamic equilibrium, temperature, zeroth law, reversible and irreversible processes, heat,work and internal energy, first Law, Carnot cycle, heat engines, heat pumps, refrigerators.
• Second Law,entropy, determination of entropy changes, direction of natural processes, dU = TdS - PdV for quasistatic processes.
• Microscopic v. macroscopic pictures, order and disorder, fluctuations, counting microstates for distinguishable particles, the Boltzmann distribution, possible and most probable distributions, energy and temperature,partition function, Boltzmann-Planck equation, the connection between thermodynamics and statistical mechanics
• Statistical properties of solids, 2-level systems, Schottky specific heat anomalies, paramagnetism, lattice vibrations and contribution to the heat capacity, defects in solids.
• Thermodynamic potentials, Helmholtz function, enthalpy, Gibbs function; throttling process; Maxwell relations; TdS equations.
• Phase changes and phase diagrams, phase equilibria, Clausius-Clapeyron equation, first and second order phase transitions, Ehrenfest classification; real gases, van der Waals equation, the critical point, Joule-Kelvin effect.
• The Third Law in positive and negative versions.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS252: Introduction to Experimental Lab

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits
• Pre-requisites: College Mathematics and Physics.

### Course Description

This module is specifically for physics non-majors only, Natural Science & exchange students.

To teach students techniques of experimental data collection and analysis, ethical standards in a scientific investigation, health and safety.

To teach how to assess the statistical validity of data and their interpretation.

To teach basic principles of electric circuit analysis, damping and resonance in electric circuits and mechanics, illustrated by experiment.

To provide students with the general and IT skills required for the manipulation and presentation of data, log book and report writing.

### Educational Aims

On successful completion of this module students will be able to:

collect experimental data using a variety of common instruments;

exhibit a practical experience of experimental methods;

perform a statistical assessment of the validity of experimental observations and the validity of their model interpretation;  to show a working knowledge of the basic principles DC and AC circuit analysis, transient response and resonance in mechanics and electric circuits. Apply their physics knowledge and problem-solving skills to model problems in science; systematically record their work in a log book; work independently and also co-operatively with colleagues; report their results in written form; discuss the role of health and safety in scientific experimentation; demonstrate high ethical standards during a scientific investigation.

### Outline Syllabus

Experimental practical laboratory and essential physics skills

This part includes lectures which teach the basic concepts of statistical analysis of data and uncertainties, ethical behaviour, the role of health and safety in scientific experimentation, IT skills including the preparation of documents, and the basic principles of DC and AC circuit analysis, transients and resonance in the context of mechanics and electrical circuits. There are five 3-hour

laboratory sessions, where students perform experiments in optics, mechanics and electric circuits which illustrate and compliment the taught material. In the final week, students are required to write a scientific report (with guidance) on one of the experiments.

Basic experimental skills. Making measurements, assessing errors and uncertainties, systematic and random errors, recording data, keeping log books, report writing. Propagation of uncertainties.

Statistical analysis of data. Mean, median, standard deviation. Normal (Gaussian) and Poisson distributions.

The role of health and safety in scientific experimentation.  Ethical behaviour in science.

Word processing, including the insertion of tables and graphics into a document, with MS Word and LaTeX.

Coursework: 100%

## PHYS254: Experimental Lab II

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: Normally PHYS 253.

### Course Description

This module requires students to reinforce and apply their experimental skills, developed in the introductory module Experimental Lab I, to assignments that are usually open ended.  Students will complete experiments involving an element of choice in method and apparatus.  Students will gain a range of skills including the organisation and execution of experimental investigations through accurate and thorough record keeping, and will strengthen their skills in critical analysis and discussion of results. Additionally, students will gain experience in application of a methodology to a variety of experimental techniques and will enhance their knowledge in identification, estimation and combination of experimental errors.

### Educational Aims

During this module, students will develop the following skills:

• organisation and execution of experimental investigations
• accurate and thorough record keeping
• critical analysis and discussion of results
• application of a methodology to a variety of experimental techniques
• identification, estimation and combination of experimental errors

### Outline Syllabus

A full list of experiments will be published at the beginning of the module. A report is written on one of the completed assignments.

Students who join the laboratories later than 253 will be able to undertake experiments from the PHYS253 and PHYS254 modules during the timetabled PHYS255 module. The experiments are more demanding than those in PHYS253 and students are encouraged to take two sessions to complete them. While none of the experiments will be compulsory, students can consult the Head of Class to choose the most useful experiments for their intended vocations. There will also be the opportunity to use computer graphics to compare experimental results with theoretical predictions.

### Assessment Proportions

• Coursework: 100%

## PHYS255: Experimental Lab III

• Terms Taught: Summer Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 253 and/or PHYS 254.

### Course Description

This module is a further expansion to the skills developed in previous modules, Experimental Lab I and II. Students will reinforce their abilities in organisation and execution of experimental investigations, and will produce accurate and thorough record keeping. This module aims to enhance students skills in critical analysis and discussion of results along with knowledge in the identification, estimation and combination of experimental errors. Students will learn to apply techniques to one or two extensive investigations.

### Educational Aims

During this module, students will consolidate the following skills:

• organisation and execution of experimental investigations
• accurate and thorough record keeping
• critical analysis and discussion of results
• identification, estimation and combination of experimental errors
• application of techniques to one or two extensive investigations.

### Outline Syllabus

A full list of experiments will be published at the beginning of the module. A report is written on one of the completed assignments.

In this module students are normally expected to take multiple laboratory sessions to complete experiments, and possibly even develop them.

### Assessment Proportions

• Coursework: 100%

## PHYS256: Experimental principles of particle detection

• Terms Taught: Summer Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS133 – 135(Normally suitable only for Physics Majors).

### Course Description

This module introduces traditional nuclear and particle physics. Experiments consist of a particle detector and readout chain with digital data processing. Students will present experimental methods and techniques to their peer group and write a report on one of their experiments.

Through conducting experiments in nuclear and particle physics, students will gain further experimental skills. Additionally, students will learn how to use particle detectors and commonly used readout electronics, and will develop their expertise in statistical data analysis and uncertainty calculation.

### Educational Aims

On successful completion of this module students will be able to:

• explain the principles of particle detection;
• display knowledge of the electronic readout chain and signal processing;
• perform a statistical analysis of a large data sample;
• explain the methods and techniques they used to their peers;
• be able to write a scientific report;
• critically review statistical analyses presented to them;
• verbally explain experimental methods and techniques.

### Outline Syllabus

Students will work singly or in pairs on two typical experiments in nuclear and particle physics.

Experiments available include:

• the measurement of the angular distribution of cosmic rays,
• the measurement of nuclear spectra with NaI-counters
• the measurement of momentum conservation in positronium decays.

Experimental equipment will consist of a particle detector and readout chain with digital data processing. For each experiment, students will have 12 hours available. Students will present the experimental methods and techniques they used to their peers. A written report is required on one of the experiments.

### Assessment Proportions

• Coursework: 100%

## PHYS263: Astronomy

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: College Mathematics and Physics.

### Course Description

This module provides students with a modern perspective on the Universe, including its size and structure. Students will investigate electromagnetic radiation and will gain an understanding of telescopes and their limitations. The module will also present basic ideas of orbits, Kepler's Laws and common astronomical phenomena in the Solar System which are orbit related.

Additionally, students will make various observations on the structure of the Sun, and will develop their knowledge of distant objects, including different types of galaxies, interacting galaxies, active galaxies and exotic objects, whilst contrasting historical models of the Universe.

### Educational Aims

On completion of this module students should:

• be familiar with our understanding of planets, stars and galaxies and how this developed;
• understand the properties and uses of electromagnetic radiation in an astronomical context;
• know how telescopes are designed and built;
• understand the physical laws of orbital motion and the phenomena which they give rise to;
• know how to characterise and classify stars.

### Outline Syllabus

• Introduction;
• Telescopes;
• Development of modern astronomy;
• Orbital physics and orbital phenomena;
• Stellar characteristics;
• Hertzsprung-Russell diagrams;
• Galaxies;
• Solar system.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS264: Astrophysics I

• Terms Taught: Summer Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 100 or equivalent and PHYS 283.

### Course Description

Students will receive an overview of directly measurable physical characteristics of stars, such as luminosity, spectroscopy, stellar atmospheres and composition. The module covers the Hertzsprung-Russell diagram and physics of Stellar Stability, and students will learn about energy generation in stars, energy transport in stellar interiors, and star birth. Students will develop the ability to demonstrate how classical physics is successful in modelling many properties of main sequence stars and in explaining their formation and evolution. Additionally, more complex stellar behaviour that cannot be understood on the basis of classical physics will be introduced. Students will gain the skillset required to perform calculations relating to gravitational collapse, stability, lifetime and energy generation in well-behaved main sequence stars and in nebulae.

### Educational Aims

On completion of the module, students should:

• have a broad knowledge of the physical characteristics of the different types of star and nebulae, and the techniques by which they are determined.
• understand the basic physical principles of stellar stability, energy production and energy loss.
• be able to perform simple calculations relating to gravitational collapse, stability, lifetime and energy generation in well-behaved main sequence stars and in nebulae.
• be able to describe, as far as is possible using only classical physics, how stars are born and evolve.

### Outline Syllabus

• Overview of directly measurable physical characteristics of stars: Mass, luminosity, spectroscopy, stellar atmospheres, temperature, pressure, composition.
• Hertzsprung-Russell diagram, stellar population and stellar evolution, importance of studying binaries and clusters.
• Physics of Stellar Stability (main sequence): Gravitationally bound systems, ideal gases. Hydrostatic equilibrium, Virial Theorem.
• Estimating central pressure and temperature. Conditions for stellar stability, effects of gas pressure and radiation pressure.
• Energy generation in stars: Gravitational contraction, thermonuclear fusion, basic principles. Comparison of energy released and timescales for different stellar collapse processes and fusion processes.
• Energy transport in stellar interiors: Radiative diffusion, photon scattering mechanisms, random walk statistics, convection, conduction.
• The Sun: A typical main sequence star closely observed. The standard model, variation of physical properties with depth. Helioseismology.
• Star birth: The interstellar medium, Jeans criterion for collapse of a nebula, protostars, formation and detection of planetary systems.
• Evolution off the main sequence: Giant stars, pulsating variables. Limits to classical models for describing collapsing stellar cores.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS265: Cosmology I

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 223.

### Course Description

The module covers the structure of the Universe from the modern perspective, examining its size and structure, galaxies and galaxy clusters, dark matter and cosmic length and mass scales. Students will learn methods of measuring astronomical and cosmological distances and Hubble's Law of Expansion.  Students will additionally encounter topics such as cosmic microwave radiation and physical phenomena in the very early universe, known as the Big Bang, through a mixture of lectures and seminars.  Finally, the module will discuss the Universes ultimate fate.

### Educational Aims

On completion of this Module the student will be familiar with:

• the structure of the Universe from the modern perspective,
• cosmological length and mass scales,
• the expansion of the Universe and its ultimate fate,
• cosmological parameters and models,
• phenomena in the very early Universe, the Big Bang.

### Outline Syllabus

• Today's picture of the Universe. Its size and structure. Galaxies and galaxy clusters, dark matter. Cosmic length and mass scales.
• Methods of measuring astronomical and cosmological distances. Apparent and absolute magnitude and luminosity. Cepheids, supernovae, galactic velocities and redshifts.
• Hubble's Law of expansion. Age and size of the Universe. Olbers' Paradox. The scale factor. Expansion of the Universe and Friedmann's equation. Newtonian derivation of the Friedmann equation.
• Main cosmological parameters: the Hubble parameter, the critical density, the mass-energy density, the deceleration parameter and the cosmological constant. Geometry of the universe, its evolution and fate.
• The theory of the Big Bang. Cosmic microwave radiation. Physical phenomena in the very early Universe.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS273: Mechanics and Variations

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 100, PHYS 110 or equivalent, PHYS 211.

### Course Description

The module develops students knowledge of Newton's laws, central forces, integrals of motion and dynamics and orbits. Students will gain an insight into generalised coordinates and momenta, Hamiltonian function, Poisson brackets and canonical transformations. The module also features lectures on important analytical methods used both in classical mechanics and in broader areas of theoretical and mathematical physics. Students will develop the ability to integrate equations of motion for dynamical problems in classic mechanics, and will have experience in using  variational methods, in addition to gaining the knowledge required to relate Hamiltonian and Lagrangian approach to theoretical mechanics and canonical transformations. Students will be able to exploit the generality of Lagrangian and Hamiltonian techniques by using an appropriate generalised coordinates.

### Educational Aims

On completion of the module, students should be able to:

• to integrate equations of motion in one and two dimensions
• to describe rotation of a rigid body
• to use variational methods and to relate Hamiltonian and Lagrangian approach to theoretical mechanics and canonical transformations.

### Outline Syllabus

• Newton's laws, central forces, dynamics and orbits, integrals of motion.
• Solution of one-dimensional dynamical problems, linear and non-linear oscillators.
• Lagrangian, its relation to Newton's equations and the least action principle.
• Rotation of a rigid body. Symmetries and conservation laws.
• Variational technique and Lagrange equations.
• Generalised coordinates and momenta, Hamiltonian function, Poisson brackets and canonical transformations.
• Phase space, stability of motion and chaos.

Special features:

This module includes lectures on analytical methods used both in classical mechanics and in broader areas of theoretical and mathematical physics.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS274: Classical Fields

• Terms Taught: Summer Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 100, PHYS 110 or equivalent, PHYS 211, PHYS 221.

### Course Description

Students will gain an insight into general integrational relations between current and charge sources, along with electromagnetic potentials in free space. This module explores energy and momentum of electromagnetic fields and the use of the Poynting vector to calculate radiated power. Students will investigate the electromagnetic power radiated by an accelerating charge and oscillating dipole, and explore wave solutions of Maxwell's equations in free and bounded space. This module will provide an understanding of the behaviour of electromagnetic modes in perfectly conducting rectangular and cylindrical waveguides and cavities. On completion, students will be able to describe EM fields with simple sources and boundary conditions, and will write down conservation laws in differential and integral form. In addition, students will develop the ability to  calculate the power radiated from accelerating charges, in particular from an oscillating dipole, in addition to reinforcing their understanding of the mode structure of EM fields in simple bounded regions, such as waveguides and cavities.

### Educational Aims

On completion of the module, students should be able:

• to display a basic knowledge and understanding of classical fields;
• to show a working knowledge and understanding of boundary conditions and conservation laws in differential and integral
• form;
• to apply the techniques used in classical fields to tackle some common problems such as the power radiated from accelerating charges, the mode structure of EM fields in simple bounded regions (waveguides and cavities) and plasma waves.

### Outline Syllabus

• General integral relations between current and charge sources and EM potentials in free space.
• Energy and momentum of EM fields and the use of the Poynting vector to calculate radiated power.
• Conservation laws in differential and integral form.
• The notion of retarded potentials.
• The EM field of an accelerating point charge.
• EM power radiated by an accelerating charge and an oscillating dipole.
• Wave solutions of Maxwell's equations in free and bounded space.
• Behaviour of EM modes in perfectly conducting rectangular and cylindrical waveguides and cavities.
• Difference between TE, TM and TEM propagating modes.
• Two-fluid model of plasmas.
• Dispersion relations for plasma waves.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS281: Scientific Programming and Modelling Project

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 100 and PHYS 110.

### Course Description

Introducing programming basics, this module engages students with the writing and compiling of computer programs in JAVA that can be used for numerical simulation and data analysis. This will involve variable types, input and output, and mathematical functions. Students will become familiar with debugging: the identification and classification of programming errors, and will explore method arguments and signatures, in addition to gaining knowledge of one dimensional, multi-dimensional and passing arrays. Students will gain the necessary knowledge to model simple physical systems using appropriate programming techniques, and will develop an understanding of numerical precision and accuracy. By learning Object Orientated programming, students will use objects and methods to represent physical systems, class design, class testing and documentation in order to independently complete an open-ended project to model a physics-based problem.

### Educational Aims

• to teach computer programming in JAVA
• to allow students to undertake an individual open-ended investigation of a physics problem using computational methods
• to teach the fundamental concepts underlying many computer languages
• to give students experience in working independently on open-ended project work
• to develop existing problem-solving skills
• to further develop skills in report writing

### Outline Syllabus

Programming basics:

• writing and compiling simple programs
• variable types
• input and output
• mathematical functions

Debugging:

• The identification and classification of programming errors.
• - Iteration, for, while, do-while loops, and nested loops.

Methods:

• arguments and signatures.

Arrays:

• one dimensional,
• multi-dimensional,
• passing arrays.

Numerical Methods:

• using programs to solve numerical problems
• using numerical integration as an example.

Object Orientated programming:

• Using objects and methods to represent physical systems,
• class design,
• class testing
• documentation

Modelling Project:

• using object orientated coding to model a 2-dimensional physical system.

Introduction to computational approximations such as the Euler Method.

### Assessment Proportions

• Coursework: 100%

## PHYS311: Particle Physics

• Terms Taught: Michaelmas Term only.
• US Credits: 4 Semester Credits.
• ECTS Credits: 8 ECTS Credits.
• Pre-requisites: Normally suitable only for Physics Majors. Requires 2nd year core Physics courses.

### Course Description

The module explores symmetries, the Quark model and gives an introduction to QCD. Students will explore leptons, as well as forces and their carrier particles and Feynman diagrams. The module aims to provide a general introduction to theoretical and experimental topics in elementary particle physics, essentially the Standard Model of particle physics.

Students will gain the ability to describe the main features of the Standard Model of particle physics and understand its place in physics as a whole, and will be able to identify major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used, such as accelerators and detectors. In addition, students will understand the role of symmetry and conservation laws in fundamental physics, and will develop the ability to perform calculations of physically observable quantities relevant to the subject, along with solving problems based on the application of the general principles of particle physics.

### Educational Aims

Knowledge and Understanding: on successful completion of the module students should be able to:

• (i) describe the main features of the Standard Model of particle physics and understand its place in physics as a whole;
• (ii) describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used (accelerators and detectors);
• (iii) understand the role of symmetry and conservation laws in fundamental physics;

Skills: on successful completion of the module students should be able to

• (i) perform simple calculations of physically observable quantities relevant to the subject;
• (ii) solve problems based on the application of the general principles of particle physics, e.g. use conservation laws to explain whether specific particle reactions and decays are allowed or forbidden;

### Outline Syllabus

Revision of Special Relativity:

• 4-vector manipulation, Center of mass energy calculations, Boosts.

Quarks and Leptons:

• Standard Model, Fermions  Bosons, Particles,  Anti Particles, Free Particle Wave Equation, Helicity States, Quark  Lepton Flavours.

213 Interactions  Fields:

• Feynman Diagrams, Electromagnetic Interaction, Strong Interaction, Electroweak Interaction, Interaction Cross-section, Decays  Resonances.

Invariance Principles and Conservation Laws:

• Parity, Parity of pions, Particles, Anti Particles, Charge conjugation, Baryon Lepton Conservation.

Quark Model:

• Baryon Decuplet, Baryon Octet, Light Pseudo-Scalar Mesons, Vector Mesons, Tests of the Quark Model.

Lepton and Quark Scattering:

• e +e to mu +mu , e +e to hadrons, Electron-muon scattering, Neutrino-electron scattering, Deep inelastic scattering.

QCD:

• Colour Quantum Number, QCD at short and long distances, Jets, Running couplings.

Weak Interactions:

• Lepton Universality, Helicity of the neutrino, V-A, Weak currents, Pion and muon decays, Weak decays of quarks, GIM model and CKM matrix, Neutral kaons.

Electroweak Interactions:

• Neutral Currents, Intermediate Vector Bosons, Couplings of quarks and leptons, Neutrino scattering, Total and Partial Widths of the Z, Higgs Mechanism.

Beyond the Standard Model:

• Supersymmetry, Neutrino Oscillations.

Accelerators Detectors:

• Accelerator operations, Interactions of particles with matter,

Basic detector elements:

• ionisation chamber, proportional counter and gas amplification, scintillators and photomultipliers, devices for position and momentum measurements, Particle identification systems, electromagnetic and hadronic calorimeters, Muon systems, Modern large multi-purpose detector systems for experiments in Particle Physics.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS313: Solid State Physics

• Terms Taught: Lent Term only.
• US Credits: 4 Semester Credits.
• ECTS Credits: 8 ECTS Credits.
• Pre-requisites: Normally suitable only for Physics Majors. Requires Level 2 core Physics courses.

### Course Description

The module offers an introduction to reciprocal lattice and diffraction of waves, the electronic band structure in metals, and insulators and semiconductors. Students will explore electrons in semiconductors, effective mass and the heat capacity of solids. There will be a summary of experimental phenomena, tunnelling, Josephson Junctions and an outline of BCS theory.

Students will be introduced to theoretical and experimental topics in solid state physics at an advanced level, and will develop an understanding of the main features of the physics of electrons in solids, along with knowledge of the main features of the optical properties of solids.

Students will gain an enhanced understanding of crystal lattices and phonons, along with the main features of the thermal properties of solids, and will be able to describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used.

### Educational Aims

Knowledge and Understanding: on successful completion of the module students should be able to:

• describe the main features of the physics of electrons in solids;
• describe the main features of the optical properties of solids
• describe the main features of crystal lattices and phonons;
• describe the main features of the thermal properties of solids;
• describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used;

Skills: on successful completion of the module students should be able to

• perform simple calculations of physically observable quantities relevant to the subject;
• solve problems based on the application of the general principles of solid state physics.

### Outline Syllabus

• Reciprocal lattice and diffraction of waves.
• Electrons and electronic band structure in metals, insulators and semiconductors.
• Tight binding and nearly-free electron models.
• Electrons in metals.
• Fermi energy and Fermi surface.
• Electron scattering processes.
• Electrons in semiconductors.
• Effective mass.
• Holes.
• Intrinsic and extrinsic behaviour.
• Junctions and devices
• Low dimensional structures, interfaces, Qwell, MQW superlattices, Qdots Optical properties, excitons,impurities, radiative and non-radiative recombination Cyclotron resonance magnetic effects, Landau levels
• Quantum Hall effect.
• Phonons.
• Acoustic and optic modes.
• Heat capacity of solids.
• Thermal conductivity of insulators.
• Phonon scattering processes.
• Superconductivity.
• Meissner effect Metallic and high Tc superconductors.
• Summary of experimental phenomena.
• Tunnelling.
• Josephson Junctions.
• Outline of BCS theory.
• Phenomenology of solid state magnetic phenomena: paramagnetism and Curie law, diamagnetism.
• Van Vleck's diamagnetism.
• Brief outline of ferromagnetism and antiferromagnetism.
• Ferromagnetic exchange and the Heisenberg model.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS321: Atomic Physics

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 223.

### Course Description

This module introduces one-electron atoms and the spin-orbit magnetic interaction, along with identical particles and the Helium atom. Students will investigate the Fermi gas model and the single particle shell model, and will compare predictions of the shell model for nuclear spins, parities and magnetic moments with experimental results. The module explores the nuclear beta decay process and the Fermi and Gamow - Teller selection rules, and students are provided with a description of the beta decay rate and the electron energy spectrum in terms of a nuclear matrix element and a statistical factor.  Students will develop their knowledge in atomic and nuclear physics to an advanced level, and will be able to use the results of basic quantum mechanics to explain the basic characteristics of atomic and nuclear structure, in addition to gaining the ability to describe the processes of atomic transitions and nuclear decays. The module will provide an explanation of the concept and importance of the parity of an atomic or nuclear state, and will provide students with the opportunity to study the nuclear beta decay process and in particular the neutrino and parity non-conservation.

### Educational Aims

This module aims to:

• to teach atomic and nuclear physics at a level appropriate for third and fourth year honours students.
• to use the results of basic quantum mechanics to explain the basic characteristics of atomic and nuclear structure and to describe the processes of atomic transitions and nuclear decays.
• to explain the concept and importance of the parity of an atomic or nuclear state.
• to study the nuclear beta decay process and in particular the neutrino and parity non conservation.

### Outline Syllabus

• Revision of "one electron" atoms and the spin-orbit magnetic interaction.
• Identical particles and the Helium atom.
• Atoms with more than one electron in the outer shell, L - S (Russell - Saunders) and j - j coupling approximations.
• Application of quantum mechanics to atomic transitions and selection rules for decay processes.
• Nuclear structure and stability, evidence for shell structure, the Fermi gas model and the single particle shell model.
• Predictions of the shell model for nuclear spins, parities and magnetic moments compared with experimental results.
• The nuclear beta decay process.
• The Fermi and Gamow - Teller selection rules.
• A description of the beta decay rate and the electron energy spectrum in terms of a nuclear matrix element and a statistical factor.
• Parity non - conservation and the neutrino.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS322: Statistical Physics

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 233.

### Course Description

This module explores the ideas, techniques and results of statistical physics. Students will examine gases and the density of states, along with the statistics of gases, fermions and bosons and the two distributions for gases. Maxwell-Boltzmann gases, velocity distribution and Fermi-Dirac gases are investigated as the module provides an uncomplicated and direct approach to the subject, using frequent illustrations from low temperature physics. Students will provide a unified survey of the statistical physics of gases, including a full treatment of quantum statistics, gaining a fuller insight into the meaning of entropy. Students will gain knowledge in applications of statistics to various types of gas. Ultimately, students will develop the ability to apply expressions and distributions in order to form accurate deductions, for example using the Boltzmann distribution for the probability of finding a system in a particular quantum state. Additionally, students will learn the role of statistical concepts in understanding macroscopic systems, and will be able to describe superfluidity in liquid helium, Bose-Einstein condensation and black body radiation.

### Educational Aims

On completion of the module, students should be able to:

• describe the role of statistical concepts in understanding macroscopic systems;
• deduce the Boltzmann distribution for the probability of finding a system in a particular quantum state;
• deduce the Einstein and Debye expressions for the heat capacity of an insulating solid and compare the theory with accepted
• experimental results;
• deduce the equation of state and the heat capacity of an ideal gas.
• deduce the Fermi-Dirac and Bose-Einstein distributions;
• describe superfluidity in liquid helium, Bose-Einstein condensation and black body radiation.
• deduce the heat capacity of a electron gas.

### Outline Syllabus

• Introduction. Review of the ideas, techniques and results of statistical physics. Revision to application to an assembly of localised particles. The Boltzmann distribution.
• Gases. The density of states - fitting waves into boxes.
• Statistics of gases. Fermions and bosons. The two distributions for gases.
• Maxwell-Boltzmann gases. Velocity distribution.
• Fermi-Dirac gases. Electrons in metals and semiconductors. Fermi energy. Liquid helium-3.
• Bose-Einstein gases. Bose-Einstein Condensation. Superfluid helium-4.
• Phoney Bose-Einstein gases. Photon gas and black-body radiation. Phonon gas and thermal properties of solids.
• Astrophysical applications. White dwarf stars, neutron stars.

Special features:

The module provides an uncomplicated and direct approach to the subject, using frequent illustrations from low temperature physics.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS323: Physics of Fluids

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 110, PHYS 211 and PHYS 213.

### Course Description

Introducing continuum mechanics, this module focuses on body and contact force, global balance laws, and decomposition of the contact force into shear and pressure components.  Students will explore static fluids, ideal fluids and the Euler equation. The module then examines Newtonian fluids, waves and the two-fluid model of plasmas. Students will be introduced to fluid dynamics and its applications within physics, and will develop an understanding of the origin, solution and application of Navier-Stokes equations, along with the wider applications of the Navier-Stokes theory to bio-, geo- and astrophysical systems. Students will also solve problems based on the application of the general principles of the physics of fluids.

### Educational Aims

Knowledge and Understanding: on successful completion of the module students should be able to

• (i) understand the origin, solution and application of the Navier-Stokes equations;
• (ii) understand the wider applications of the Navier-Stokes theory to bio-, geo- and astrophysical systems;

Skills: on successful completion of the module students should be able to

• (i) perform simple calculations of physically observable quantities relevant to the subject;
• (ii) solve problems based on the application of the general principles of the physics of fluids

### Outline Syllabus

• Introduction to continuum mechanics : mass, body force, contact force, global balance laws, decomposition of the contact force into shear and pressure components, particle trajectories, comoving coordinates, local balance laws and the continuity equation.
• Static fluids: contact force in static fluids, equations of global and local hydrostatic equilibrium and their solutions in simple scenarios, derivation of Archimedes' principle.
• Ideal Fluids: the Euler equation, incompressibility, steady flow and streamlines, Bernoulli's H-theorem and applications, vorticity and irrotational flow, circulation, Kelvin's circulation theorem and its application to tornados, vortex lines, comparison with magnetostatics, potential flow, no-through-flow boundary condition, fluid contact force on rigid bodies and d'Alembert's paradox with examples.
• Newtonian fluids: Stress tensor, Newton's law of viscosity, Navier-Stokes equations, no-slip boundary condition, difficulties with solving the Navier-Stokes equations and the importance of computational fluid dynamics, Reynolds' number and hydrodynamic similarity, boundary layers, vortex shedding and resolution of d'Alembert's paradox, Kutta-Joukowski lift formula and flight, vortex induced vibration.
• Waves : compressible fluids, equations of state, linearised solutions to the fluid equations, gravity waves and their dispersion, acoustic waves and the speed of sound.
• Fluid mechanics of plasmas: Two-fluid model of plasmas, stationary approximation for the ions, linearisation of the cold plasma equations, Langmuir oscillations and the plasma frequency, electromagnetic waves in plasmas and their dispersion, group velocity of signals in plasmas, application to long-range communication and pulsar distance measurements.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS351: Semiconductor Physics Laboratory

• Terms Taught: Michaelmas Term only
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 130, PHYS 250 or equivalent.

### Course Description

Students will be introduced to the physics of semiconductors through a series of experimental investigations. This module provides an opportunity for students to write an individual report on one of the experiments conducted, which may include band theory and/or relation to optical and electronic behaviour of solids. The Shockley-Haynes experiment, transport properties drift and carrier lifetime will be covered in the module, in addition to topics such as important semiconductors, impurities and both direct and indirect band gaps. By the end of the module, students will understand the basic principles of semiconductor physics and related semiconductor physics. They will be able to demonstrate the main techniques of optical spectroscopy and reinforce their knowledge of various physical concepts involved in the description of solid state behaviour. Students will also become acquainted with some of the most important types of semiconductors through working with Si, Ge, GAA and will gain a practical understanding of  semiconductor properties, in addition to acquiring basic spectroscopy experience. Students will also apply concepts of band theory to analysing optical and electronic properties of common semiconductors.

### Educational Aims

At the end of this laboratory module, the student should:

• have become acquainted with some of the most important types of semiconductors through working with Si, Ge, GaAs
• have obtained hands-on experience of using optical methods to analyse semiconductor properties have acquired basic spectroscopy experience
• have applied the concepts of band theory to analysing optical and electronic properties of common semiconductor be able to record their work in a logbook
• have developed report writing skills.

### Outline Syllabus

This module is designed to introduce the interesting physics of semiconductors through a series of experimental investigations. The course runs for 1 day per week for 5 weeks. At the end of the course, students are required to write an individual report on one of the experiments.

• Band theory and relation to optical and electronic behaviour of solids. Shockley-Haynes experiment, transport properties drift, diffusion, recombination, carrier lifetime and mobility.
• Important semiconductors and band structure, silicon, germanium, gallium arsenide.
• Impurities, n and p-doping, p-n junction, diode equation and diode behaviour.
• Direct and indirect band gaps. Properties of light emitting diodes and photo-detectors.
• Basic spectroscopy techniques. Analysis of electroluminescence and optical absorption data and determination of refractive index.

### Assessment Proportions

• Coursework: 100%

## PHYS352: Low Temperature Physics Laboratory

• Terms Taught: Lent Term only
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 130, PHYS 250 or equivalent.

### Course Description

This module provides an introduction to low temperature experimentation. Students will learn how to perform experiments and use cryogenic liquids safely, and will discover some of the basic physics investigated in the experiments, as well as receiving a tour of the ultra-low temperature physics laboratory. Some of these experiments include a paper exercise to design an experimental cryostat insert for experiments at 4K, an experimental investigation of the suitability and use of thermometers over the temperature range from room temperature to near 1K and an experimental study of the novel second sound mode (temperature wave) in superfluid 4He. Students will devise and perform any additional measurements which they think might give further insights into the physics investigated, before writing a formal report on one of the experiments. Additionally, students will gain the ability to recognise and discuss the properties of superfluids and superconductors.

### Educational Aims

This module aims:

• to provide an experimental background to lecture courses in low temperature physics
• to develop skills in the safe handling of cryogenic apparatus
• to investigate the suitability of different thermometers for different temperature regimes
• to investigate the behaviour of superfluids and low temperature superconductors
• to develop team-working skills
• to further develop skills in writing a scientific report

### Outline Syllabus

Introduce the interesting physics of matter at low temperatures. In the first week, an introduction is given to low temperature experimentation including how to perform experiments and use cryogenic liquids safely, a discussion of some of the basic physics investigated in the experiments, a visual demonstration of some of the exotic properties of superfluid 4He and a tour of the ultra-low temperature physics laboratory. In subsequent weeks, students will work in small groups and undertake a different one-day mini-project each week.

These include:

• A paper exercise to design an experimental cryostat insert for experiments at 4K. This gives a basic grounding in how to design apparatus for experiments at lower temperatures.
• An experimental investigation of the suitability and use of thermometers over the temperature range from room temperature to near 1K.
• An experimental study of the novel second sound mode (temperature wave) in superfluid 4He.
• Experiments on superconductivity.
• Two characteristic phenomena of superconductivity are investigated experimentally, namely zero resistivity and magnetic flux exclusion (Meissner effect).
• Experiments on superfluid turbulence using vibrating wire resonators.
• Measurement of the normal fluid component of superfluid 4He using an aerogel experiment (this is analogous to the famous Andronikashvili experiment).

Students are encouraged to devise and perform any additional measurements which they think might give further insights into the physics investigated. At the end of the module, students are required to write a formal report on one of the experiments including a general discussion of the cryogenic techniques employed and a background to the physics investigated.

### Assessment Proportions

• Coursework: 100%

## PHYS353: Particle Physics Group Project

• Terms Taught: Michaelmas and Lent / Summer Term only.
• US Credits: 5 Semester Credits.
• ECTS Credits: 10 ECTS Credits.
• Pre-requisites: PHYS 130, PHYS 250 or equivalent.

### Course Description

This module will provide guidance on project management, planning and meetings. There will be a planning stage in which groups of students will assign the roles of the team members, perform initial research and develop plans in terms of tasks, deliverables and timing including a Gantt chart. Plans will be presented to the rest of the class in a group presentation, with feedback given by the lecturer. At the end of the project, groups will prepare a group report and give an individual talk at the third year mini-conference.  Students will develop skills in the safe use of nuclear detectors and sources, and will undertake an open-ended investigation of a particle physics-based problem. The module also aims to introduce students to the tasks associated with a research project in particle physics,  Students will use nuclear particle detectors and sources, with the aim to develop a research project with formulation, literature searches, data gathering, analysis and presentation.

### Educational Aims

On completion of this module, students will be able to:

• Use nuclear particle detectors and sources.
• Develop a research project with formulation, literature searches, data gathering, analysis and presentation.
• Work co-operatively as part of a team.
• Have skills required to pursue an open ended project.
• Have the ability to record their work in a log-book.
• Write a scientific report

### Outline Syllabus

The Particle Physics Group Project involves an open-ended investigation of a problem related to Particle Physics Detectors. There is no set syllabus and the problem - in general terms - will be defined by the lecturer. Typically, this may be done either by stating the broad requirements of a solution within certain constraints or by posing an open-ended question related to a physical phenomenon. The project will not be tightly-restrained by defined limits, allowing for adaption and many different solutions to a given problem.

Students will work as part of a team (typically 4-5) and will submit a group report.

Projects vary from year to year, but examples of project areas may include:

Gamma spectroscopy.

• What are differences, strengths and applications of plastic scintillators, NaI crystals and HPGe?
• What is the radioactive contamination of sand samples at the north west coast of England?
• Can we find nuclear isotopes from the Fukushima incident in the air?

Angular correlation.

• Investigate the consequences of quantum mechanics in nuclear decays: energy and momentum conservation, choice of quantisation axis.
• Determine the speed of gamma rays.

Cosmic rays. Investigate cosmic rays:

• What is the angular distribution and composition of cosmic rays?
• Does the rate of cosmic rays depend on the elevation, humidity, air pressure or other parameters?
• Can we confirm Einstein's theory of special relativity using cosmic muons?
• What is the muon lifetime?

Z0 boson and weak interaction.

• What are the decay modes of the Z0 boson?
• How can one identify electrons, muons, taus and quark-jets?
• What are the branching ratios?
• How can one distinguish between electron-positron scattering and electron-positron annihilation?
• How many light neutrino generations are there?

### Assessment Proportions

• Coursework: 100%

(Group Report 55%, Log Book 15%, Peer Assessment 15% & Presentation at the PLACE – student conference 15%)

## PHYS354: Physics Literature Search

• Terms Taught: Michaelmas and Lent Term only.
• US Credits: 4 Semester Credits.
• ECTS Credits: 8 ECTS Credits
• Pre-requisites: (PHYS 252if taking in Lent) - This course is for non-Physics majors.

### Course Description

This dissertation module provides students the opportunity to study in depth a topic in physics which they have. Where possible, there will be a link to the subject of the final year project. The preparation of the dissertation will involve considerable use of Library facilities for directed literature searches of research material. The completed dissertation will be word-processed and students will be expected to master software packages for the presentation of results and figures.

Students will be required to use information retrieval and storage systems, and will be expected to gather, assimilate, organise, understand and summarise relevant information in order to write a scientific document which contains reference to the sources, reveals a structured view of the subject, conveys some understanding and summarises the topic. Students will develop the ability to defend the written presentation orally if required, and thereby give further evidence of understanding.

### Educational Aims

On completion of a literature search the student should be able to:

• use information retrieval and storage systems
• gather, assimilate, organise, understand and summarise relevant information
• write a scientific document which contains reference to the sources
• reveals a structured view of the subject
• conveys some understanding and summarises the topic
• defend the written presentation orally if required, and thereby give further evidence of understanding

### Outline Syllabus

There is no set syllabus, literature searches vary from year to year and are tailored to suit the individual student(s) and the available supervisors. Topics are suggested by students or by staff and the title and area are chosen well in advance.

### Assessment Proportions

• Coursework: 100%

## PHYS361: Cosmology II

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 265.

### Course Description

The module explores the global dynamics of the Universe, the Friedmann equation, energy conservation and acceleration equations. The constituents of the Universe content and their evolution with time are then investigated. Students will examine the early Universe and the radiation era of the Hot Big Bang. The thermal history of the Hot Big Bang cosmology and Cosmic Inflation is studied as part of the module, along with the formation of large-scale structure (galactic clusters and super-clusters) in the Universe. Students will develop awareness of our current understanding of the observed Universe and the early Universe, and will be able to write down some of the equations that encode this understanding. Students will also follow new developments at the level of journals like Nature and Scientific American.

### Educational Aims

On completion of this module the student will:

• be aware of our current understanding of the observed Universe and the early Universe.
• be able to write down some of the equations that encode this understanding.
• be able to follow new developments at the level of journals like Nature and Scientific American.

### Outline Syllabus

• The global dynamics of the Universe.
• The Friedmann equation. Energy conservation and acceleration equations.
• The constituents of the Universe content and their evolution with time.
• The early Universe.
• Thermal equilibrium.
• Decoupling of relics.
• The cosmic microwave background (CMB).
• Monopole and dipole moments of the CMB.
• Neutrino decoupling.
• The radiation era of the Hot Big Bang.
• Adiabatic expansion and the timescale.
• The formation of the first nuclei one second after the Big Bang.
• Matter-antimatter annihilation.
• The mystery of the baryon asymmetry.
• Thermal history of the Hot Big Bang cosmology.
• Phase transitions in the early Universe.
• The formation of nucleons.
• The emergence of electromagnetism.
• The breaking of grand unification.
• Cosmic Inflation and the solution of the horizon and flatness problems of Big Bang cosmology.
• How inflation can provide the source for the formation of structures (e.g. galaxies) in the Universe.
• Primordial temperature anisotropy in the CMB and structure formation.
• The formation of large-scale structure (galactic clusters and super-clusters) in the Universe.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS362: Astrophysics II

• Terms Taught: Lent Term only.
• US Credits: 2 Semester Credits.
• ECTS Credits: 4 ECTS Credits.
• Pre-requisites: PHYS 264.

### Course Description

Providing an expansion to topics covered in Astrophysics I, this module teaches students about stellar structure and stability, before moving on to thermonuclear fusion and stellar collapse. Students will discover degenerate objects, such as white dwarves and neutron stars, and will investigate x-ray and high energy astrophysics. By the end of the module, students will understand the contributions of modern physics, notably quantum mechanics, nuclear and particle physics and relativity, to current understanding of stars and astrophysical phenomena. Students will also be able to describe recent astrophysical discoveries and review phenomena observed through the latest technological advances. Ultimately, students will gain knowledge in the contributions of modern physics, notably quantum mechanics, nuclear and particle physics and relativity, to our understanding of stars and astrophysical phenomena, and will gain an awareness recent astrophysical discoveries and review phenomena observed through the latest technological advances.

### Educational Aims

On completion of the module the student should:

• appreciate how each area of classical and modern physics has a role to play in the description of stellar behaviour and other astrophysical phenomena,
• understand for each topic the basic physical principles and relate them to the observed characteristics, and
• be able to follow and place in context general articles in astrophysical literature.

### Outline Syllabus

• Basic principles: stellar structure and stability.
• Thermonuclear fusion:
• Principles, main sequence, hydrogen burning, CNO and pp cycles, helioseismology, solar neutrinos, neutrino oscillations, ITER.
• Later stages of stellar fusion: helium and carbon burning, origin of light and heavy nuclei.
• Stellar collapse:
• Schonberg-Chandrasekhar limit, formation of white dwarf, variable stars, Cepheids. Supernovae, Type I, accreting binary system, use as a standard candle. Type II, collapse of a supergiant, shell burning, role of neutrinos, supernova remnants, Crab nebula, SN 1987a.
• Degenerate objects
• Degeneracy. White dwarf, Fermi system. Chandrasekhar limit, Neutron star formation, basic principles, physical characteristics. Pulsars, identification with neutron star, mechanism of radiation.
• Binary systems:
• Detached and semi-detached. Orbits. Classical novae, X-ray pulsars, millisecond pulsars, the binary pulsar, the double pulsar.
• Gamma ray bursters.
• Current issues: Cosmic rays, gravitational waves, X-ray astronomy.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS363: Astrophysics Laboratory

• Terms Taught: Michaelmas Term only
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS
• Pre-requisites: PHYS 361, PHYS 264.

### Course Description

This module will familiarise students with astronomical experimentation and instrumentation. This includes practical use of a telescope, CCD cameras as well as manipulation of images taken with such instrumentation. Computer simulations will develop students understanding of key concepts in observational astronomy and students are encouraged to devise and perform any additional measurement or modelling which they think might give further insights into the physics investigated. The laboratory is structured around a series of experiments which are intended to each last one working day. Students take a selection of these throughout the five weeks of the module. At the end of the module, students are required to write a more in-depth report on just one of the weekly activities, supported not only by the results they obtained but also demonstrate additional reading into the physics and astronomy to which the work relates. On completion, students will be able to make simple measurements using the telescope, spectroscope and CCD camera, in addition to developing an understanding of basic astronomical phenomena through computer simulations. Students will gain an appreciation for the statistical nature of astrophysical knowledge through analysis of stellar data relating to luminosity and temperature, and will be acquainted with some of the problems involved in satellite-based activities.

### Educational Aims

On completion of this module the student will:

• Understand the basic principles of, and be able to make simple measurements using the telescope, spectroscope and CCD camera
• Reinforce understanding of basic astronomical phenomena through computer simulations
• Appreciate the statistical nature of astrophysical knowledge through analysis of stellar data relating to luminosity and temperature.

### Outline Syllabus

The purpose of this laboratory course is to familiarise students with astronomical experimentation and instrumentation. This will include practical use of a telescope, CCD cameras as well as manipulation of images taken with such instrumentation.

There are also computer simulations that will develop understanding of key concepts in observational astronomy. The manual is intended only for guidance and during the experimental work, students will be encouraged to devise and perform any additional measurement or modelling which they think might give further insights into the physics investigated. Students will find the techniques learnt here useful for future possible MPhys projects. Possible experiments may include:

• An experiment-based workshop reviewing the basic optical principles of telescopes, and the various factors that determine their performance - field of view, focal length, magnification, aberrations.
• Computer-based simulation of astronomical measurements illustrating some important aspects of stellar and galactic astronomy: e.g. stellar parallax, Cepheid variable stars, mass determination from visual and eclipsing binary stars, and the distribution of mass in a galaxy from galactic rotation curves.
• Practical experience in using a CCD (charge-coupled device) camera and in processing images. The standard laboratory suite of acquisition and software analysis tools will be used to process a library of images taken with the telescope, correct image faults and create composite colour images.
• Astronomical data processing activities giving experience in working with real data relating to the Hertzsprung-Russell diagram and variable star photometry. Raw CCD images will be calibrated and manipulated leading to the time evolution of the magnitude of a variable star, reinforcing the concept of magnitude and the relationship with the observed number of photons.

### Assessment Proportions

• Coursework: 100%

## PHYS364: Cosmology Group Project

• Terms Taught: Lent & Summer Terms only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 361.

### Course Description

Students will work as part of a team and will receive guidance on project management, planning and meetings. Students will prepare a group report and will also give an individual talk at the third year mini-conference, in addition to developing a research project with formulation, literature searches, data gathering, analysis and presentation. The module provides an understanding of modern cosmology, including the areas where our understanding is still incomplete. In addition, students will investigate an open-ended Cosmology-based problem and will gain awareness of the tasks associated with a research project in Cosmology.

### Educational Aims

On completion of this module, students will be able to:

• Understand the basics of current research topics in Cosmology.
• Develop a research project with formulation, literature searches, data gathering, analysis and presentation.
• Work co-operatively as part of a team.
• Demonstrate the importance of communication skills in presentation of results.

### Outline Syllabus

The Cosmology Group Project involves an open-ended investigation of a Cosmology-based problem. There is no set syllabus and the problem - in general terms - will be defined by the lecturer. Typically, this may be done either by stating the broad requirements of a solution within certain constraints or by posing an open-ended question related to a physical phenomenon. The project will not be tightly-restrained by defined limits, allowing for adaption and many different solutions to a given problem. Projects vary from year to year, but examples of projects may include a description of the Age of the Universe problem and its resolution via a cosmological constant or dark energy. Students will work as part of a team (typically 4-5) and will submit a group report.

### Assessment Proportions

• Coursework: 100%

(Group Report 55%, Log Book 15%, Peer Assessment 15% & Presentation at the PLACE – student conference 15%)

## PHYS366: Groups and Symmetries

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 110, PHYS 232.

### Course Description

The module will cover various topics, such as symmetries and transformations; groups, group invariants and generators. As well as this, students will learn about irreducible representations; orthogonal groups O(2) and O(3); unitary groups SU(2) and SU(3) and applications to spin, isospin, colour and flavour of elementary particles. By the end of the module, students will have a basic knowledge and understanding of the concepts and methods used in group theory. They will be able to apply these concepts and methods to problems in particle physics, cosmology and field theory.

### Educational Aims

On successful completion of the module students should be able to:

• Display a knowledge and understanding of the concepts of transformation , invariance and symmetry and their mathematical descriptions;
• show a knowledge of the foundations of group theory and the specific properties of orthogonal and unitary groups;
• apply this knowledge to various problems in particle physics and cosmology.

### Outline Syllabus

The module will cover various topics including:

• symmetries and transformations;
• groups, group invariants and generators;
• irreducible representations;
• orthogonal groups O(2) and O(3);
• unitary groups SU(2) and SU(3);
• applications to spin, isospin, colour and flavour of elementary particles.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS367: Flavour Physics

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 311.

### Course Description

The module will cover various topics including CKM matrix and its parameterisations; unitarily constraints and the unitarity triangle and the status of experimental measurements, theory and observations of neutrino oscillations. Students will also study CP violation and current topics of heavy flavour physics, such as c- and b-hadron production and decay analysis, along with top quark physics. Students will develop a basic knowledge of the phenomenology of flavour mixing in the quark sector, neutrino oscillations and will gain an awareness of the concepts of transformation, invariance and symmetry and their mathematical descriptions. Additionally, students will reinforce their understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations, in addition to gaining knowledge of some current topics on the physics of heavy flavours which are likely directions of the experimental particle physics research in Lancaster.

### Educational Aims

On successful completion of the module students should be able to:

• Display a knowledge and understanding of the basic ideas, concepts and analyses of the experimental data on flavour mixing in weak interactions of hadrons and neutrino oscillations;
• display a knowledge of some current topics on the physics of heavy flavours which are likely directions of the experimental particle physics research in Lancaster.

### Outline Syllabus

The module will cover various topics including:

• CKM matrix and its parameterisations;
• unitarity constraints and the unitarity triangle;
• status of experimental measurements;
• theory and observations of neutrino oscillations;
• CP violation;
• current topics of heavy flavour physics, such as c- and b-hadron production and decay analysis, top quark physics.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS375: Theoretical Physics Independent Study

• Terms Taught: Michaelmas and Lent Terms only.
• US Credits: 3 semester credits
• ECTS Credits: 6 ECTS
• Pre-requisites: PHYS 211, PHYS 213, PHYS 273, PHYS 274,

### Course Description

This module requires students to undertake an independent study in various aspects of theoretical physics. It provides an opportunity for students to extend their preliminary studies by undertaking open-ended investigations into various aspects/problems of theoretical physics. Students will write up their findings in a report. This module aims to teach analytical recipes of theoretical physics used in quantum mechanics, with the focus on the variational functions method, operator techniques with applications in perturbation theory methods and coherent states of a quantum harmonic oscillator. Students will be trained in the use of the operator algebra of 'creation' and 'annihilation' operators in the harmonic oscillator problem, which will develop a basis for the introduction of second quantisation in many-body systems. In addition, the module will introduce the algebra of creation and annihilation operators for Bose and Fermi systems, along with second-quantised representation of Hamiltonians of interacting many-body systems. Students will learn to apply a mathematical basis of complex analysis in order to solve problems in mathematical and theoretical physics. They will also analyse Bose-Einstein condensation in one-, two-, and three-dimensional systems and will develop the ability to describe the condensate using the method of coherent states. Additionally, the module will reinforce students knowledge of the Ginzburg-Landau theory and the vortices in a superfluid.

### Educational Aims

On successful completion of this module students will be able to:

• Use the variational principle in application to quantum mechanical problems.
• Apply the operator algebra of creation and annihilation operators to study non-harmonicity effects in quantum oscillators.
• Use coherent states in order to relate quantum and classical motion of harmonic systems.
• Perform calculations using Pauli matrices.
• Operate with the algebra of creation/annihilation operators for Bose and Fermi gases.
• Write down the Hamiltonian describing an interacting Bose/Fermi gas in the second-quantised representation.
• Describe Bose-Einstein condensation.
• Use the condensate wave function to describe the origin of vortices in a superfluid/superconductor.
• Apply complex analysis to problems in physics, including the evaluation of definite integrals.
• Retrieve and digest scientific information from various sources.
• Manage a number of different tasks successful.
• Write a scientific report.

### Outline Syllabus

Analytical Recipes:

• Relation between the Schrodinger equation and matrix formulation of quantum mechanics and the variational principle.
• Energy and energy functional.
• Minimisation of functionals under constraints and Lagrange multipliers.
• Practical training in the use of the variational function approach.
• Operators and commutation relations.
• Creation and annihilation operators in the harmonic oscillator problem.
• Anharmonicity in nonlinear oscillators, use of creation and annihilation operators in perturbation theory calculations.
• Evolution operator in quantum mechanics, use of the evolution operator in applications to the harmonic oscillator problem.
• Coherent states as eigenstates of annihilation operators.
• Properties of coherent states and classical dynamics of wave packets modelled using coherent states.

• Second quantisation operators for Bose and Fermi statistics, operator algebra of creation and annihilation operators.
• Local operators, their commutation properties, completeness of the single-particle basis.
• Hamiltonians of interacting many-body systems in the second quantised representation.
• Bose-Einstein condensation from the statistical physics point of view. Bose-Einstein condensate as a coherent state of a Bose gas.
• Ginzburg-Landau theory of a super uid phase transition.
• Vortices in a super uid.
• Ultracold atomic gases and BEC in atomic traps.
• Gauge invariance.
• Ginzburg-Landau theory of superconductivity

Complex analysis:

• analytic functions, Cauchy-Riemann conditions.
• Contour integrals, Cauchy's theorem, Cauchy's integral formula.
• Laurent series, poles, residues.
• The residue theorem, methods of finding residues, evaluation of definite integrals.
• Applications in Physics.

### Assessment Proportions

• Coursework: 100%

## PHYS379: Theoretical Physics Group Project

• Terms Taught: Lent & Summer Term only.
• US Credits: 5 semester credits
• ECTS Credits: 10 ECTS
• Pre-requisites: PHYS 375

### Course Description

The aims of this module are:

To prepare students to enable them to undertake fourth year theoretical physics projects.

To give students experience in team activity and in open-ended project work.

To develop information retrieval skills.

To enhance existing problem solving skills.

To further develop skills in report writing and presentation.

### Educational Aims

On successful completion of this module students will be able to

Tackle open ended projects.

Keep a log-book.

Retrieve and digest scientific information from various sources.

Manage a number of different tasks successful.

Write a scientific report.

Establish co-operative working practices with colleagues.

Give a verbal presentation about their research.

### Outline Syllabus

The project involves an open-ended investigation of a Theoretical Physics-based problem. There is no set syllabus and the problem in general terms - will be defined by the lecturer. Typically, this may be done either by stating the broad requirements of a solution within certain constraints or by posing an open-ended question related to a physical phenomenom. The project will not be tightly restrained by defined limits, allowing for adaption and many different solutions to a given problem. Projects vary from year to year, but examples of projects may include modelling the properties of electrons in crystal lattices (graphene, topological insulators, Kitaev lattice); dynamics of vortices in superfluids and/or superconductors; particles obeying fractional statistics; problems in mathematical

physics. Students will work as part of a team (typically 4-5) and will submit a group report.

### Assessment Proportions

Coursework: 100%

(Group Report 55%, Log Book 15%, Peer Assessment 15% & Presentation at the PLACE – student conference 15%)

## PHYS384: Physics of Living Systems

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS.

### Course Description

The aims of this module are:

• To introduce the topic of biomedical physics, and to show how physical principles help one to understand the function of living systems at all levels of complexity - starting at the molecular, via the cellular, to the organ and system levels.
• To introduce stability analysis of thermodynamically open systems.
• To convey an appreciation that living systems are structures in time as much as structures in space.
• To provide an introduction to coupled oscillatory processes characteristic of living systems.
• To introduce some analytical techniques for analysis of data related to complex, oscillatory systems.

### Educational Aims

On successful completion of this module students will be able to

• explain the basic characteristics of living systems as thermodynamically open systems.
• explain the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems.
• apply their knowledge of physics and mathematics to the understanding of basic principles of living systems starting from a cell to the cardiovascular system and the brain.

### Outline Syllabus

• 1. Introduction and revision of physics concepts that will be needed
• 2. What is life?
• 3. Stability and synchronization in complex and open interacting systems
• 4. Entropy and information; DNA as an information storage system
• 5. Fundamental rate processes: Boltzmann equation
• 6. Molecular diffusion and Brownian motion
• 7. Ion channel dynamics
• 8. Cellular structure and function: passive and active transport across a cell membrane
• 9. Membrane potential: Nernst-Planck and Goldman equations
• 10. Oscillatory dynamics of membrane potential
• 11. Action potential: Hodgkin-Huxley equations
• 12. Integrate and fire model and functioning of the brain as an information-processing system
• 13. Mechanical and electrical properties of the heart
• 14. Functioning of the cardiovascular system as a system that provides energy and matter to cells
• 15. Oscillations and turbulence in blood flow
• 16. Interactions between cardiovascular oscillations and brain waves

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS388: Energy

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 233.

### Course Description

The module introduces students to energy demand in the past, present and future, looking at energy use by sector and country. Students will study thermal power stations, nuclear power and take a planetary view of energy sources. From there, the module moves to renewable energy, costing energy and looking at Hydrogen as a fuel for the future. Students will consider energy use in the home and at work, looking at energy efficiency and alternative small-scale energy sources. By the end of the module, students will gain a broad overview of energy and the issues involved from a physical basis, and will be able to clearly explain the physics of energy and global warming and make an informed contribution to the debate.

### Educational Aims

On completion of the module, students should be able to:

• clearly explain the physics of energy and global warming and make an informed contribution to the debate,
• apply their knowledge of physics to solve practical energy problems,
• cost capital projects on a small and large scale,
• review and criticise science issues with a high public profile.

### Outline Syllabus

• Introduction: Energy demand past, present (and future), energy use by sector, country.
• Thermal power stations: Thermodynamics and heat engines, heat pumps, internal combustion engines, turbines and electricity generation, electricity supply and coping with variable demand.
• A planetary view: planetary energy sources, planetary effective temperature and natural greenhouse effect, anthropogenic greenhouse gas emissions and global warming (based on IPCC),dissenting views and climate modelling.
• Nuclear power: fission  fusion reactions, operation and types of fission reactors, nuclear fuel cycle, nuclear fusion reactors, is nuclear power a viable solution to global warming?
• Renewable energy: Ultimate sources of renewable energy (how much is there), overview of renewable sources, wind power, wave power, tidal power, hydroelectricity, solar cells (conventional Si  GaAs concentrator cells), integrating renewables.
• Costing energy: Capital costs  discounting, costs of electricity generation
• Hydrogen, fuel of the future?: Oil, gas and coal reserves, fuel cells, hydrogen production and storage.
• Energy use at home and at work: Energy efficiency (insulation, appliance efficiency, condensing boilers etc.), alternative small-scale energy sources (combined heat and power, solar hot water,micro wind and hydro, heat pumps), costs and grants, personal carbon trading.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS389: Computer Modelling

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 281 or equivalent.

### Course Description

Building on the skills developed in the Scientific Programming and Modelling Project (PHYS281), this module will introduce students to new elements of Java, and will involve more sophisticated modelling of physical systems, such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.  Students will develop a more thorough knowledge of the java language, including the use of inheritance, and will be able to write a physics modelling program in java.

### Educational Aims

On completion of the module, students should:

• Have a more thorough knowledge of the JAVA language, including the use of inheritance and polymorphism.
• Have an appreciate of numerical algorithms for modelling physical systems.

### Outline Syllabus

Brief lectures will be given in the early part of the course to introduce new elements of Java as required. Most of the time will be spent on working through a series of exercise in modeling physical systems such as calculating the range of a cannon ball, and simulating the motion of the moon around the earth.

### Assessment Proportions

• Coursework: 100%

## PHYS390: Space and auroral physics

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 222 or MATHS equivalent.

### Course Description

In this module you will exploit general concepts and skills developed in electromagnetism and apply them to natural space environments to gain an understanding of the controlling plasma physics. This module will enhance your skills in problem solving and the synthesis of research level material.

### Educational Aims

On completion of this module the student will have an understanding of the Earths upper atmosphere and be able to explain the role of solar electromagnetic radiation in the formation of the ionosphere and the plasma physics that controls ionospheric structure and dynamics. The student will also be able to demonstrate an understanding the coupling between the terrestrial atmosphere/magnetic field and the near-Earth space environment. In addition to the physical mechanisms and the consequence of this coupling in terms of natural phenomena, such as the aurora borealis, the student will be able to understand their impact on human technology (so-called

space weather).

### Outline Syllabus

Solar activity and its influence on interplanetary space.

Introduction to the solar-terrestrial environment.

The Earths neutral atmosphere.

The formation and physics of the Earths ionosphere and its layers.

Collisional and collisionless plasmas.

Ionospheric conductivity and its control of ionospheric currents.

Charged particle precipitation and plasma processes controlling the aurora borealis and terrestrial radiation belts.

The role of geomagnetic storms and substorms on energy transfer within the Sun-Earth system.

The causes and impacts of space weather.

Coursework: 20%

Exam: 80%

## PHYS411: Advanced Relativity and Gravity

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 225, PHYS 211, PHYS 213 or MATHS equivalent.

### Course Description

The module offers a short review of special relativity, tensor calculus on Minkowski spacetime, differential calculus on Minkowski spacetime, and curved spacetimes. Students will explore general relativity, gravity as intrinsic curvature of spacetime, and the Einstein equations, along with predictions of the linearized Einstein equations, gravitational waves, and gravitomagnetic field equations. Students will investigate exact solutions of the Einstein equations, black holes and event horizons. By the end of the module, students will have a basis knowledge and understanding of the theories of special and general relativity, and possess a conceptual understanding of the links between Newtonian mechanics and relativity. The module also provides a geometrical insight into the properties of space-time and relativity.

### Educational Aims

On completion of this module students should be able to:

• Display a knowledge and understanding of the basic principles of special and general relativity;
• describe and perform relativistic calculations;
• display some geometrical insight into the properties of space-time;
• display good problem solving skills.

### Outline Syllabus

• Weak and Strong Equivalence Principles,
• spacetime,
• the line element,
• functionals and calculus of variations,
• proper time functional and Newton's 2nd law,
• gravitational potential and the metric,
• geodesics, tensors,
• Christoffel symbols,
• covariant derivative,
• intrinsic curvature,
• equation of geodesic deviation,
• Einstein field equation,
• Schwarzschild spacetime,
• gravitational redshift,
• precession of planetary orbits,
• gravitational lensing,
• black holes,
• cosmological spacetimes
• gravitational waves.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS412: Experimental Methods in Particle Physics

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS311.

### Course Description

Students will study particle detection and experiments, exploring discoveries in particle physics and statistical tests, electroweak symmetry breaking and the Higgs mechanism. The module allows students to investigate CP violation and neutrino oscillations, and provides an introduction to supersymmetry and extensions to the standard model of particle physics. By the end of the module, students will reinforce their knowledge and understanding of particle physics, and will gain a basic knowledge of experimental measurement and analysis techniques used in modern day particle physics research. Students will also develop an awareness of some recent advancements and current problems in particle physics research, and will go on to describe the successes and weaknesses of the standard model of particle physics and the possible theoretical extensions.

### Educational Aims

At the end of the module, the student should be able to:

• Display a knowledge and understanding of the principles of particle detection and measurement;
• describe and perform basic calculations of statistical tests used in experimental particle physics;
• describe the successes and weaknesses of the standard model of particle physics and the possible theoretical extensions;
• display good problem solving skills.

### Outline Syllabus

• Particle Detection and Experiments,
• discoveries in Particle Physics and statistical tests,
• electroweak symmetry breaking and the Higgs mechanism,
• CP violation and neutrino oscillations,
• introduction to supersymmetry and extensions to the standard model of particle physics.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS462: Gauge Theories

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS362.

### Course Description

To teach the modern phenomenology of the Standard Model of fundamental particles. To provide the mathematical background and physical insight into the field-theoretical structure of the Standard Model. To give an awareness of modern developments in Quantum Field Theory.

### Educational Aims

On completion of the module, students should be able to understand:

Display a knowledge and basic understanding of the ideas and concepts behind the field-theoretical description of the Standard Model of fundamental particles; show a knowledge of future prospects for the Standard Model including gauge theories of the strong and electroweak interactions.

### Outline Syllabus

The module will cover various topics including:

Lagrangians and gauge transformations; global and local gauge invariance; gauge group and its representations; QED as a gauge theory; QCD and non-abelian theories; asymptotic friedom; renormalisation group equation; spontaneous symmetry breaking and Higgs mechanism; gauge structure of the electroweak theory; grand unified theories; extensions of the Standard Model.

Coursework: 20%

Exam: 80%

## PHYS463: Solar-Planetary Physics

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS362.

### Course Description

Students will extend their knowledge on planetary systems, looking at the advances in planetary physics and planetary radiation environments. The module explores solar-planetary coupling and planetary magnetospheres, planetary magnetospheres within our solar system and unmagnetised bodies, such as Mars, the moon and comets. Students will study the heliosphere and beyond, investigating the suns influence on cosmic rays. This module introduces students to the physical processes that dominate and characterise the planets in our solar system and those postulated to exist beyond.  This will include the terrestrial planets, the outer planets and moons, the physics of planetary exploration, planetary astrophysics and the implications for life in the universe. Students will be required to carry out independent research on pre-set discussion topics and present their findings to the group in the form of oral presentations and posters in a series of seminars. Students will be able to explain the key similarities and differences between the planets in the solar system, and will understand the role of a planets magnetic field in the retention of a gaseous atmosphere. Students will gain further skills such as the ability to calculate the scale size of a planets magnetosphere, and a developed knowledge of the important role of comparative planetology in our understanding of the solar system .In addition, students are required to undertake orbital mechanics calculations relevant to planetary systems and exploration.

### Educational Aims

On completion of the module, students should be able to understand:

• Explain the key similarities and differences between the planets in the solar system (rocky/gaseous, magnetic/non magnetic).
• Explain the role of a planets magnetic field in the retention of a gaseous atmosphere.
• Calculate the scale size of a planets magnetosphere.
• Explain the important role of comparative planetology in our understanding of the solar system.
• Undertake orbital mechanics calculations relevant to planetary systems and exploration
• Realise the importance of combining in-situ and remotely-sensed measurements of planetary environments.

### Outline Syllabus

• Planetary systems
• Exploring the planets and advances in planetary physics
• Solar-planetary coupling and planetary magnetospheres
• Planetary magnetospheres within our solar system (Earth, Mercury, Jupiter and Saturn).
• Planetary ionospheres, comparative planetology and extra-terrestrial aurora. Internal plasma sources (moons) in magnetospheres and co-rotation v convection driven magnetospheres
• Unmagnetised bodies. Mars and the Moon. Comets.
• The heliosphere . The Suns influence on cosmic rays. Beyond the heliosphere

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS464: Astrophysics III : Galaxies

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits
• Pre-requisites: PHYS362 & PHYS264.

### Course Description

This module will enhance your skills in problem solving and the synthesis of advanced research level material. The module will also provide you with an understanding of how various forms of data may be generated and analysed, both qualitatively and quantitatively.

### Educational Aims

On completion of this module the student will have an understanding of the physics that regulates galaxy formation and evolution.

They will be able to explain the theoretical descriptions and observations of active galaxies, and be able to demonstrate an understanding of the different observational techniques required to detect radiation from a range of astrophysical sources.

Students will also study the links between the measurements of galaxy properties and the broader, cosmological picture required in order to build an understanding of some of the most fundamental questions about the Universe that lie at the forefront of current observational astrophysics.

### Outline Syllabus

The structure of galaxies. The formation of galaxies, including our Milky Way and its satellites, in a cosmological context. Physics of galaxy formation and evolution. Galaxy scaling relations. Feedback processes including supernovae. Quasars and Active Galactic Nuclei their physics and observability (observations in X- and -rays, radio). Black holes in galactic centres. The interstellar medium.

Nucleosynthesis and galactic chemical evolution. The star formation history of the universe, from the first galaxies to now. Large scale structures, galaxy clusters. Observational techniques for measurement of cosmological parameters.

### Assessment Proportions

Coursework: 20%

Exam: 80%

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS313.

### Course Description

Students will be offered a revision of elements of the theory of electromagnetism, before being introduced to the phenomenology of solid state magnetic phenomena. The module discusses Van Vleck's description of diamagnetism and diamagnetism as quantum phenomenon. Students will explore ferromagnetism and antiferromagnetism, ferromagnetic exchange and the Heisenberg model, which includes self-consistent mean field theory. A description of ferromagnetic phase transitions and Curie temperature will be provided as part of the module, along with the elements of the Ginzburg-Landau theory of magnetic phase transitions.  By the end of the module, students will develop a knowledge and understanding of magnetic and electric phenomena in condensed matter physics, in addition to an enhanced awareness of recent advances and current problems in condensed matter physics.

### Educational Aims

On completion of this module students should be able to:

• display knowledge and basic understanding of magnetic and electronic phenomena in condensed matter;
• solve selected model problems requiring advanced methods from condensed matter theory;
• show an increased awareness of some recent advances and current problems in condensed matter physics;
• delve deeper into the published literature on recent advances in condensed matter physics;
• display good problem solving skills which are transferrable to other areas of physics (in particular, areas utilising quantum
• mechanics and advanced methods from statistical physics);
• progress to graduate study in condensed matter physics.

### Outline Syllabus

• Revision of elements of the theory of electromagnetism: Magnetic field, magnetic induction, magnetic vector potential. Magnetic field of magnetic dipole moment.
• Phenomenology of solid state magnetic phenomena: paramagnetism (Curie law), diamagnetism. Van Vleck's description of diamagnetism, diamagnetism as quantum phenomenon. Ferromagnetism and anti-ferromagnetism. Ferromagnetic exchange and the Heisenberg model, self-consistent mean field theory.
• Description of ferromagnetic phase transitions, Curie temperature. Elements of Ginzburg-Landau theory of magnetic phase transitions. Domains and domain walls. Ferromagnetic insulators and metals. Magnetic memory devices and readheads. Multilayers of normal and ferromagnetic metals, giant magneto-resistance phenomenon and its application.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS482: Quantum transport in Low Dimensional Nanostructures

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS313.

### Course Description

Students can expect to explore two-dimensional electron systems, quantum transport in disordered low-dimensional electron systems and semiconductor quantum wires. The Büttiker-Landauer conductance formula is investigated, focusing on impurities in quantum wires, electronic transport in a magnetic field and the Hall effect. The module considers metallic point contacts, the point-contact spectroscopy of the electron-phonon interaction, and atomic break-junctions and the scanning tunnelling microscope. Students will receive examples of applications of scanning tunnelling microscopy as part of the module. By the end of the module, students will have knowledge of the physics of nanoscale solid state devices and how these may be manufactured and utilised. They will enhance their awareness of the recent advancements and current problems in condensed matter physics.

### Educational Aims

On completion of this module students should be able to:

• display knowledge of the physics of nanoscale solid state devices and how these may be manufactured and utilised;
• solve selected model problems requiring advanced methods from condensed matter theory;
• show an increased awareness of some recent advances and current problems in condensed matter physics;
• delve deeper into the published literature on recent advances in condensed matter physics;
• display good problem solving skills that are transferrable to other areas of physics (in particular, areas utilising quantum mechanics and advanced methods from statistical physics);
• progress to graduate study in condensed matter physics.

### Outline Syllabus

Two-dimensional electron systems:

• heterostructures, quantum wells, field-effect transistors, graphene.
• Conductivity and resistivity.
• Drude formula for conductivity and the Einstein relation.
• Electron scattering and the role of disorder.
• Screening of impurities in metals.
• Friedel oscillations of electron density around impurities.

Quantum transport in disordered low-dimensional electron systems:

• interference and the enhanced backscattering of waves in disordered media, localisation effect in two- and one-dimensional electron systems.
• Universal conductance fluctuations in small phase-coherent conductors.
• The Aharonov-Bohm effect in small ('mesoscopic') metallic and semiconductor rings.
• Semiconductor quantum wires (1D subbands in quantum wires).
• Carbon nanotube as an ideal one-dimensional conductor.
• Ballistic wires in semiconductors structures and the conductance quantum.
• The Büttiker-Landauer conductance formula.
• Impurities in quantum wires.
• Electronic transport in a magnetic field, Hall effect.
• Skipping orbits and electron focusing.
• Landau levels. Edge states of Landau level as ideal one-dimensional conductors.
• Quantum Hall effect and its relevance for metrology.
• Metallic point contacts.
• The point-contact spectroscopy of the electron-phonon interaction.
• Atomic break-junctions and the scanning tunnelling microscope.
• Examples of applications of scanning tunnelling microscopy.
• Semiconductor quantum dots.
• Resonance tunnelling phenomenon.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS483: Quantum information processing

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS223.

### Course Description

The module consolidates the theoretical concepts of quantum information processing, exploring Dirac notation, density matrices and evolution, and entanglement. Students will also explore qubits, quantum algorithms, circuit design and error connection. In addition, the module will address trapped ions and atoms, Josephson junctions and quantum optics. By the end of the module, students will be familiar with the fundamental concepts of quantum processing, such as density matrices and the dynamics of quantum systems, and will be able to understand how these can be implemented in realistic devices. Students will learn about experimental implementation based on atom-optical realisations and realisations in the solid state, and will apply these to explore theoretical concepts that have a vast area of application in condensed matter physics and atom-quantum-optics.

### Educational Aims

On completion of this module students should be able to:

• demonstrate familiarity with fundamental concepts of quantum information, including qubits, superposition and entanglement, quantum circuit design and error correction;
• demonstrate familiarity with experimental implementations in atom-optics and in the solid state;
• work with advanced, efficient quantum-mechanical methods and have deepened their understanding of manipulation, control and measurements.

### Outline Syllabus

Theoretical concepts of quantum information processing:

• Revision;
• Dirac notation;
• density matrices and evolution;
• qubits;
• entanglement;
• quantum algorithms, circuit design, error correction

Illustration via discussion of experimental realizations:

• (from) trapped ions and atoms, Josephson junctions, quantum optics

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS484: Advanced Electrodynamics and Gravity

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS.

### Course Description

The aim of the module is to provide an introduction to aspects of modern differential geometry used in theoretical and mathematical physics, with specific application to electromagnetism and gravity. .

### Educational Aims

On successful completion of the module the students should be able to:

• display an understanding of the intrinsic, covariant nature of electrodynamics and a familiarity with handling the Einstein equations and field equations on curved spacetime
• formulate and tackle field theories on spacetime using tools from modern differential geometry.

### Outline Syllabus

Introduction to differential geometry and exterior calculus

• Scalar fields, vector fields, covector fields, p-forms, exterior derivative, metrics, Hodge dual, Lie derivative, connections, Bianchi identities, integration of p-forms.

Electrodynamics

• Maxwell equations in terms of the Maxwell 2-form, 4-velocity fields and Lorentz force equation in terms of the Maxwell 2-form.

Gravity

• Einstein 3-forms, stress-energy-momentum 3-forms, Einstein equations. Killing vectors, spacetimes with symmetry, conserved quantities, black holes. Action principles.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS485: Matter at low temperature

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS322.

### Course Description

The module begins by discussing what physicists mean by high and low temperatures, and looks at the different types of ordering that may occur as systems cool. Students will explore cryogenic techniques used for accessing such low temperatures are described, including the design of useful cryostats. Students will observe the new phenomena that occur when systems are cooled below room temperature and will consider electron pairing leading to the zero resistance of superconducting materials, the effect of magnetic fields, and the role of macroscopic quantum mechanical wave functions. The module provides an overview of the practical uses in superconducting quantum interference devices (SQUIDs). The module seeks to explore a selection of fascinating phenomena that occurs when cooling matter to temperatures more than a million times colder than the familiar 290K of everyday life and observe the significance for both physics and technology. Additionally, students will appreciate the relation between temperature and order, will know how low temperatures are produced, including dilution refrigerators, and will also be able to describe the phenomena of superconductivity and superfluidity.

### Educational Aims

On completion of this Optional Module the student will

• appreciate the relation between temperature and order
• know how low temperatures are produced, including dilution refrigerators
• be able to describe the phenomena of superconductivity and superfluidity

### Outline Syllabus

The course begins by discussing what physicists mean by high and low temperatures. It looks at the different types of ordering that may occur as systems cool, and asks whether it is possible to achieve an absolute zero in temperature. Then cryogenic techniques used for accessing such low temperatures are described, including the design of useful cryostats. Next we examine the new phenomena that occur when systems are cooled below room temperature. This mainly concerns superconductivity and superfluidity. We discuss electron pairing leading to the zero resistance of superconducting materials, the effect of magnetic fields, and the role of macroscopic quantum mechanical wave functions. We also look at some practical uses in superconducting quantum interference devices (SQUIDs). The macroscopic wave functions of both superfluid 4He and 3He are probed, including the existence of quantised vortices. The properties of 4He/3He mixtures and their use in dilution refrigerators are described.

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS486: Lasers and Applications

• Terms Taught: Lent Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 223, PHYS 231, PHYS 321.

### Course Description

This module will address the necessary requirements for laser action, spontaneous and stimulated emission rates, Einstein coefficients, optical gain coefficient, and characteristics of the emitted light. Students will become aware of the different types of lasers, such as gas and solid state, semiconductor, dye, chemical and excimer lasers. Semiconductor lasers: homojunction, single and double heterojunction devices will be investigated, along with materials and operating requirements. The module explores fabrication methods, quantum well lasers, advantages and characteristics. There will be a focus on a range of applications including laser surgery, optical fibre communications, laser machining, pollution monitoring and remote sensing. By the end of the module, students will be familiarised with lasers and their applications, including the operating principles of a variety of different lasers.  Students will understand the many uses of lasers in industry, medicine and the environment.

### Educational Aims

On completion of this module the student will have a broad knowledge of many aspects of lasers and their applications.

### Outline Syllabus

•  Fundamentals: properties of laser light, requirements for laser action, spontaneous and stimulated emission rates, cavity physics (matrix optics), line broadening, modes of light, Q-switching, mode-locking, second-harmonic generation.
• Laser technologies: solid-state (including fibre), gas, chemical, excimer and semiconductor lasers important examples of each will be detailed (and demonstrated where possible).
• Applications: Industrial processing, medical, telecoms, holography, LIDAR, fundamental physics (QIP, gravity wave detection, fusion).

### Assessment Proportions

• Coursework: 20%
• Exam: 80%

## PHYS487: Semiconductor Device Physics

• Terms Taught: Michaelmas Term only.
• US Credits: 3 Semester Credits.
• ECTS Credits: 6 ECTS Credits.
• Pre-requisites: PHYS 313.

### Course Description

Students will familiarise themselves with crystal growth, including growth theory, faceting, impurity segregation and zone refining. The module presents students with a silicon case study, investigating semiconducting properties, silicon oxide, masking, surface pacification and photo-lithographic processing. Compound semiconductors will be discussed, covering band structure advantages over silicon, II-VI materials and effects of iconicity.  Additionally, students will explore thin film semiconductors, such as epitaxy, vapour phase growth, metallo-organic methods and liquid phase epitaxy, and the module provides a broad inter-disciplinary overview of the linkage between the physics, chemistry and other materials sciences involved in the synthesis of semiconductors and the devices made from them.  By the end of the module, students will develop an understanding of the basic properties of crystals and crystal defects, and will be able to describe how crystals are grown and discuss the main semiconductor used for microelectronics as a detailed case study. Students will also demonstrate how physics continues to play a major role in enabling information technology.

### Educational Aims

On completion of this optional module the student will be able to:

• Give a quantitative description of the operating principles of different modern semiconductor devices.
• Gain an insight into the relevant properties of semiconductor materials and underlying aspects of solid state physics used in the design and fabrication of semiconductor devices.
• Understand the key properties of quantum wells, superlattices and quantum dots in relation to tailoring device performance

### Outline Syllabus

• Fundamental optical and transport properties of semiconductor materials;
• Band-gap engineering - how to tailor semiconductors for specific device applications;
• Operating principles of modern semiconductor devices, including for example: diode lasers, LEDs, solar cells, infrared detectors,
• high speed transistors, CCDs and memories;
• Epitaxial growth techniques for the fabrication of state-of-the-art semiconductor nanostructures and quantum devices;
• An overview of device fabrication, nanolithography, and Moores Law

### Assessment Proportions

• Coursework: 20%
• Exam: 80%