Physics

The module is compulsory in the Physics and Quantum Technology Pathways.

This module explores the applications of quantum mechanics to common themes in quantum technology. Students will understand axiomatic formulation of quantum mechanics and Dirac notation, including states and the Hilbert space, operators and their representations, the time-dependent Schrodinger equation and elements of measurement theory. Students will also develop knowledge of quantum dynamics, be able to provide examples of such, and understand their application.

Successful completion of this module will see students be able to describe concepts and formalism of quantum mechanics, collate and understand complex information taken from a range of sources, and be able to solve problems based on the application of quantum mechanics.

This module provides students with a working knowledge and understanding 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. The module addresses the basic properties of wave propagation, diffraction and inference, and laser operation.

Students will develop their skills in vector calculus and will learn to apply Maxwell’s equations in the analysis of common electromagnetic phenomena, including motors and generators, and in the fundamental connection between electricity and magnetism. Students 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.

The module is compulsory in the Physics and Quantum Technology Pathways.

This module introduces a list of eight experiments which will be published prior to the first session. Students are required to write a report on one of their completed tests, and through undertaking eight experiments, students will learn fundamental skills of measurements, uncertainties and the use of standard instruments.

By completing this module, students will demonstrate a practical understanding of experimental investigations, which involves accurate and thorough record keeping along with skills in critical analysis, presentation of results, and minimisation of experimental errors. Students will acquire knowledge of various experimental techniques and will learn how to identify, estimate, combine and quote experimental errors.

The module is compulsory in the Physics and Quantum Technology Pathways.

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.

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 module’s 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 Kronekker 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.

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.

This module covers quantum mechanics in all its generality, from its central postulates and mathematical language to concrete phenomena and applications. Students will learn how the main postulates give precise meaning to the states, observables, dynamics, and measurable properties of quantum systems, and how this translates into general features of the theory, such as its inherent probabilistic nature on the one hand, and precise quantisation of observable properties on the other. This material is introduced and developed by a series of model systems and applications, such as the particle in a box, tunneling through a barrier, the harmonic oscillator, the hydrogen atom, angular momentum and spin, driven systems displaying radiative transitions, and many-body systems exhibiting entanglement and obeying the Pauli exclusion principle. Students will also become familiar with the mathematical language of the theory, including the Dirac notation, differential and matrix operators, commutation relations, and the role of eigenvalue problems. They will also gain practice with solution techniques such as separation of variables, stationary and time-dependent perturbation theory, the Ehrenfest and Heisenberg picture. Through further applications and examples, students will acquire prerequisite knowledge for advanced courses in atomic and molecular physics, condensed matter physics, particle physics, astrophysics, and quantum information processing.

Students will receive an introductory concepts-based approach to the physics of special relativity, nuclei and fundamental particles. The module covers the general properties of nuclei, such as composition, the forces within the nucleus, mass, binding energy and nuclear decay. Students are then introduced to the standard model of particle physics, including the three generations of fundamental particles and their interactions.

Students will gain an understanding of the basis of Einstein’s theory of special relativity in electro-magnetism, both conceptually and mathematically, and 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.

Introducing programming basics, this module engages students with the writing and running of computer programs in Python for numerical simulation and data analysis. This will involve learning about variable types, flow control and logical expressions, functions, and classes. They will gain knowledge of software libraries for numerical computations, including the handling of array data formats. They will be introduced to good coding practices, such as documenting and testing their code, and become familiar with methods to debug their programs.

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 in order to independently complete an open-ended project to model a physics-based problem.

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.

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.

Students will be examined on material in core physics modules from year one, two and three. There will be a series of workshops prior to the final examination, for discussion about the types of question set on the examination paper and the revision of problem solving and modelling techniques.

The module examines basic physics principles by applying them in situations that use ideas from multiple core physics modules. This module will allow students to demonstrate a broad grasp of physics principles. Ultimately, they will be well practised in the application of physics methodology and general problem solving techniques to a wide range of problems.

The Industrial Group Project is an option in the Physics Pathway.

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, and thereby give further evidence of understanding.

This module is compulsory in the Physics and Quantum Technology Pathways.

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.

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.

The Particle Group Project is compulsory in the Particle Pathway and is an option in the Physics and the Particle with Cosmology Pathways.

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 student 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,

Use nuclear particle detectors and sources, with the aim to develop a research project with formulation, literature searches, data gathering, analysis and presentation.

The Quantum Technology Group Project is compulsory in the Quantum Technology Pathway and an option in the Physics Pathway.

This module aims to prepare students to undertake a major quantum technology project, and to enhance problem-solving skills and practical laboratory skills. The project involves students conducting an open-ended investigation of a quantum technology problem, either about a physical phenomenon, or finding different solutions to a given problem. Projects vary year on year, but examples of projects may include experimental investigation of spin manipulation and coherence using benchtop ESR/EPR, testing the performance of superconducting circuits, and theoretical simulation of a quantum computer using a PC.

On successful completion of this module, students will understand how to apply underlying physics ideas and concepts to tackle an open-ended physics problem, by planning, conducting, and reporting on the results of a quantum technology investigation. Students will also be able to demonstrate an appreciation of experimental uncertainty, conduct statistical analysis to interpret data, and present the results of their research.

This module is compulsory in the Physics and Quantum Technology Pathways.

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.

The module offers an introduction to electronic, thermal, optical and magnetic properties of solids.

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, crystal lattices and phonons, reciprocal lattice and diffraction of waves, the electronic band structure in metals, insulators and semiconductors. Students will explore electronic properties of semiconductors, including the physics of p-n junctions and their optical properties. Students will be introduced to the basics of magnetism in solids.

Students will gain an enhanced understanding of solid state physics, and will be able to describe major pieces of experimental evidence supporting the key theoretical ideas, including the experimental techniques used.

This module is compulsory in the Quantum Pathway, and is an option on the other pathways.

This module will provide students with an overview of solid-state realisations of quantum technologies, including superconductivity, low-dimensional structures, and impurity and donor systems, and introduces students to fabrication and characterisation techniques for micro-structures and nano-structures.

Students will develop skills to formulate problems in precise terms, while identifying key issues, to solve problems and provide well-defined solutions. Students will also understand how to collate and understand complex information from a range of sources, including verbal information from lectures, lecture notes, and key textbooks.

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.

Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Python, 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 Python language, including the use of inheritance, and will be able to write a physics modelling program in Python.

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.

The module is compulsory on the Particle Physics, Particle Physics with Cosmology and Theoretical Physics Pathways and an option on all others.

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.

The module is compulsory in the Astrophysics, Astrophysics with Cosmology and Astrophysics with Space Pathways.

This module provides students with a modern perspective on the Universe, including its size, structure and evolution over roughly 14 billion years. Students will be introduced to orbits, Kepler’s laws, electromagnetic radiation, telescopes and detectors and learn all the major key astronomical tools that allow us to explore the Universe from the smallest to the largest scales.

Once all the physical tools are introduced, the module explores what we know about stars, their formation and evolution, our solar system, and extra-solar planets. It then moves out to our Galaxy and our local group, and travels back in time to explore the Universe and the major events over the last 13 billion years, including with computer simulations.

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.

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.

This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an information-processing system and the interactions between cardiovascular oscillations and brain waves.

Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.

Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then 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.

The module is compulsory on the Particle Physics and Particle Physics with Cosmology Pathways and an option on all others.

This module covers various topics, including the 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 heavy flavour particle physics topics, 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 and neutrino oscillations, and they 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.

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.

The module is compulsory on the Astrophysics with Space Pathway and an option on all other Pathways.

Space and Auroral Physics explores the physics of the solar-terrestrial environment, from the solar wind, which streams from the Sun towards Earth, to how the atmosphere couples to the local space environment. This module will introduce you to basic plasma physics, the dynamics of Earth’s magnetosphere, and the formation of the aurora. It will also address the causes and impacts of space weather of technology and society.

MPhys projects vary from year to year and are tailored to suit the individual student and the available research facilities. This two-module project commences with a dissertation or literature review. Students will write a report on the project work and will conduct a presentation for the mini-conference in the summer term, along with gaining skills related to oral presentation of scientific research.

Project work gives students the opportunity to carry out research or a detailed investigation into a specific area of physics appropriate to their chosen degree theme. Students will develop and apply analytical and problem-solving skills in an open ended situation, involving use of the library, computer, and other resources as appropriate, working alone or in a small group.

By the end of this module, students will demonstrate the ability to plan, manage and execute an investigation an area of physics in a systematic way using appropriate techniques. They will formulate conclusions and critically compare with relevant theory, and may be required to generate and analyse data and critically assess experimental uncertainties.

This module introduces a range of geometry and exterior calculus, including scalar fields, vector fields and convector fields. Students will explore p-forms, exterior derivative, metrics and Hodge dual, and will discover electrodynamics, more specifically Maxwell equations in terms of the Maxwell 2-form, 4-velocity fields and Lorentz force equation in terms of the Maxwell 2-form. Gravity is also covered, and students will engage in topics such as Einstein 3-forms, stress-energy-momentum 3-forms and Einstein equations. Additionally, students will gain knowledge of killing vectors, spacetimes with symmetry, conserved quantities and black holes.

Students will gain the knowledge required to display an understanding of the intrinsic, covariant nature of electrodynamic, along with a familiarity with handling the Einstein equations and field equations on curved spacetime. Students will also be able to formulate and tackle field theories on spacetime using tools from modern differential geometry.

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.

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.

Building on the skills developed in the Scientific Programming and Modelling project, this module will introduce students to new elements of Python, 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 Python language, including the use of inheritance, and will be able to write a physics modelling program in Python.

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.

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.

The module covers various topics including Lagrangians and gauge transformations, global and local gauge invariance, gauge group and its representations and QED as a gauge theory. Students will explore QCD and non-abelian theories, asymptotic freedom and renormalisation group equation. The module discusses spontaneous symmetry breaking and Higgs mechanism, gauge structure of the electroweak theory, grand unified theories and extensions of the Standard Model.

By the end of the module, students will understand the modern phenomenology of the Standard Model of fundamental particles and will gain the mathematical background and physical insight into the field-theoretical structure of the Standard Model. Students will have an increased awareness of modern developments in Quantum Field Theory.

The module is compulsory on the Particle Physics, Particle Physics with Cosmology and Theoretical Physics Pathways and an option on all others.

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.

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.

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.

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.

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.

This module focuses on what constitutes life. It explores the stability and synchronisation in complex and open interacting systems, entropy and information, and DNA as an information storage system. Students will investigate fundamental rate processes, ion channel mechanics and molecular diffusion and Brownian motion. In addition, cellular structure and function, along with membrane potential and action potential are studied, and the module examines the functioning of the cardiovascular system as an information-processing system and the interactions between cardiovascular oscillations and brain waves.

Students will develop an awareness of how physical principles help to understand the function of living systems at various levels of complexity, as well as an appreciation that living systems are structures in time as much as structures in space.

Ultimately, the module will equip students with the ability to explain the basic characteristics of living systems as thermodynamically open systems, in addition to teaching the physical principles of the functioning of a cell, how cells make ensembles (tissues and organs), and how they interact within larger biological systems. Students will then 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.

The module is compulsory on the Particle Physics and Particle Physics with Cosmology Pathways and an option on all others.

This module covers various topics, including the 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 heavy flavour particle physics topics, 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 and neutrino oscillations, and they 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.

This module provides students with an introduction to the theory underpinning space plasmas and an understanding of how different plasma structures develop and evolve in solar and planetary systems. Students will learn how this translates into interpreting measurements and observations to infer the dynamics of remote and local space environments, for example, understanding how solar flares are generated, how the solar wind interacts with the atmosphere of Mars, and how Jupiter’s aurora are produced.

On successful completion of this module, students will be able to explain how to define a plasma and how they are characterised in solar and planetary environments, and understand how plasma structures are identified and interpreted in data. Students will be able to describe the equations of magnetohydrodynamics and use them to explain and interpret a range of space plasma phenomena, including oscillations, shock waves, and magnetic reconnection. This will enable students to be able to explain the behaviour of plasmas from the atmosphere of the Sun, to the magnetospheres of the planets (e.g., Earth, Saturn) and comets, and into the interstellar medium.

The module provides students with an introduction to non-relativistic quantum field theory and its applications to single-particle and many body systems. Students will develop knowledge of the path integral formulation of quantum mechanics for single particles, many-body systems and fields and will develop skills to perform computations with functional integrals and quantum field theory techniques in many-body physics. Field theory involves sophisticated physics concepts and mathematical formalisation, including advanced algebra and calculus, and its study requires strong skills in performing elaborate analytical calculations.

Successful completion of this module will see students be able to discuss the path integral formulation of quantum mechanics and use functional integral techniques to describe single-particle quantum effects, including quantum tunnelling, and to compute physical properties of many-body systems.

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.

Students can expect to explore the electronic properties of two-dimensional and one-dimensional materials such as graphene and carbon nanotubes. They will learn how to describe transport in disordered systems including quantum interference effects. The Landauer-Büttiker conductance formula is investigated, focusing on ballistic transport, impurities in quantum wires and the integer quantum Hall effect. The module concludes with an introduction to the concepts of geometric phase and topological insulators. By the end of the module, students will know how to describe electronic transport in low-dimensional quantum materials in various regimes, enhancing their awareness of recent advancements in cutting edge research in condensed matter physics.

This module is compulsory in the Quantum Pathway, and is an option on the other pathways.

This module will provide students with an overview of solid-state realisations of quantum technologies, including superconductivity, low-dimensional structures, and impurity and donor systems, and introduces students to fabrication and characterisation techniques for micro-structures and nano-structures.

Students will develop skills to formulate problems in precise terms, while identifying key issues, to solve problems and provide well-defined solutions. Students will also understand how to collate and understand complex information from a range of sources, including verbal information from lectures, lecture notes, and key textbooks.

The module is compulsory on the Astrophysics with Space Pathway and an option on all other Pathways.

Space and Auroral Physics explores the physics of the solar-terrestrial environment, from the solar wind, which streams from the Sun towards Earth, to how the atmosphere couples to the local space environment. This module will introduce you to basic plasma physics, the dynamics of Earth’s magnetosphere, and the formation of the aurora. It will also address the causes and impacts of space weather of technology and society.

This module provides students with experience of implementing data analysis techniques for applications across multiple fields in Physics. Students will learn the skills needed to apply a range of statistical tests to data for the purposes of hypothesis testing, and to implement multiple analysis types on real and varied data. Students will develop the skills needed to select and employ the most appropriate statistical technique for a variety of different data types to improve their physical understanding of the specific context relevant to that data.

On successful completion of this module, students will have developed key skills in processing, synthesising and distilling complex information from a variety of sources using different methods, and apply their knowledge to solve challenging problems. Students will be able to visually convey complex quantitative information in a clear and professional way.

The module is compulsory on the Particle Physics with Cosmology and Astrophysics with Cosmology Pathways and an option on all others.

The module follows the global dynamics of the Universe, the Friedmann equation, energy conservation and acceleration equations. Students will examine the early Universe, the initial singularity and the radiation era of the Hot Big Bang. The thermal history of the Hot Big Bang cosmology 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.