Supervisor
Professor Henning Schomerus
Description
Quantum systems can display robust features related to topological properties. These attain precise values that can only change in phase transitions where the states change their topological properties. While the scope of these effects is well understood for electronic and superconducting systems, a much richer range is encountered for photonic and bosonic systems. In these systems particles can be created and annihilated, which results in loss, gain, and nonlinearity. Recent years have seen a surge of activity to tailor these bosonic systems to their electronic counterparts, mostly by eliminating the mentioned differences. Going beyond these efforts, work of the supervisor and collaborators has demonstrated that topological physics extends beyond these mere analogies, leading to experimental demonstrations for laser, microwave resonator arrays, and polaritonic condensates. In parallel, a substantial body of literature has emerged on models that extrapolate topological notions to these settings.
What is missing is a fundamental understanding of the physical scope of these extension. Most models include the out-of-equilibrium effects phenomenologically, often with the desired effects already in mind. Furthermore, the characterization of the models often uses properties that do not have an immediate physical meaning. This project tackles these questions generally and practically by developing a consistent response theory that allows to derive and analyse effective models. The development of this framework will be guided by considering concrete photonic and mechanical settings. The project develops analytical and numerical skills in quantum mechanics and classical wave dynamics.
Supervisor
Professor Henning Schomerus
Description
Quantum systems can encode information, but this information quickly becomes inaccessible if the associated degrees of freedom coupled with the environment. A key recent realization points towards systematic measurements as a way to arrest this undesirable process. However, measurements induce an additional source of randomness, and fundamentally change the dynamics of the system.
This project aims at characterizing the resulting complicated dynamics by identifying universal aspects that are independent of the details of the system. This will be approached by including random elements into the dynamics, which make the systems accessible via powerful stochastic methods. Important parts of the project will be to set up suitable models that capture the key physics of relevant systems, and to identify and evaluate quantities that robustly characterize the resulting dynamics. This project develops skills describe of quantum many-body systems analytical and numerically.
Supervisor
Dr Neil Drummond
Description
Positron annihilation spectroscopies are sensitive techniques for characterising both molecules and bulk materials. When a positron annihilates with an electron in a molecule or crystal, the resulting gamma rays carry information about the local electronic structure; e.g., the positron lifetime depends on the electronic density, while the momentum distribution of the outgoing radiation depends on the electronic momentum distribution. However, positrons significantly perturb the electronic structure of the molecules to which they bind. Hence experimental positron annihilation studies rely on computational modelling to interpret the results produced.
In this project you will develop and apply quantum Monte Carlo methods for solving the many-body Schroedinger equation for positronic molecules and bulk materials to produce data that will facilitate the interpretation of positron annihilation experiments. The work will involve developing and implementing appropriate forms of trial many-body wave function and investigating the effects of nuclear motion on positronic molecules.
The project is of a theoretical and computational nature, and is suited to a student with interests in numerical modelling, scientific computer programming, materials science, and quantum mechanics.
Supervisor
Dr Neil Drummond
Description
The variational and diffusion quantum Monte Carlo (VMC and
DMC) methods are powerful and accurate techniques for solving the many-body time-independent Schroedinger equation. They are widely used in condensed matter physics and quantum chemistry to simulate the behaviour of electrons so that we can predict and understand the electronic, optical and chemical properties of molecules, materials and semiconductor devices.
The VMC and DMC methods rely on the availability of accurate and flexible many-body wave-function forms. Typical VMC and DMC calculations use Slater determinants of single-particle orbitals, multiplied by an envelope function called a Jastrow factor, with the single-particle orbitals being evaluated at points offset from the actual particle positions by a so-called backflow displacement. Both the Jastrow factor and the backflow displacement are parameterised, symmetric functions of all the particle positions.
In this project the goal is to investigate new approaches for producing appropriate trial wave functions for many-body fermionic systems by including long-range multibody terms and neural network functions of particle positions in the backflow displacement. The aim is to produce highly accurate wave-function forms that can be used to study systems of hundreds of particles. The variational principle of quantum mechanics provides the crucial measure of wave-function quality, with more accurate wave functions giving lower energy expectation values. The use of better wave functions will increase the accuracy of quantum Monte Carlo calculations of structural, optical and vibrational properties of molecules and bulk materials; these predictions can be compared with experimental measurements.
For few-body systems such as light atoms and very small molecules it will also be possible to obtain benchmark results by explicitly antisymmetrising many-body wave functions of Jastrow form. This approach can be used to study the ground-state properties of small molecules in which nuclear motion is treated on an equal footing with electronic motion, allowing a comparison of near-exact nonrelativistic quantum mechanical calculations with experiment. Such calculations could also be performed for positronic molecules to calculate positron lifetimes and hence to support positron annihilation spectroscopic measurements.
It will be interesting to compare these two approaches for generating accurate wave function forms for small molecules.
This project is theoretical and computational in nature, requiring strong computer programming skills.
