My research toward my PhD is in the field of mathematical physics, specifically in the study of anyons in quantum mechanics.
While in three dimensional quantum systems there are two classes of particles, being fermions and bosons, when two dimensional systems are studied it is known that particles may fall into a more general classification.
These particles are know as anyons because they can hold any quantum statistics, and their behaviour is characterised by a parameter between zero and one known as the fractional statistics parameter.
If this parameter is set to zero or one then bosonic or fermionic behvaiour is recovered respectively.
The worldlines of anyons form braids through 2+1-dimensions, and the exact braiding of these particles effects their quantum state.
Anyons have been used as a model for particles in order to describe a mysterious physical phenomenon called the fractional quantum Hall effect, and have been proposed as a route to fault-tolerant quantum computing due to their topological nature.
Architectures for topological quantum computers often involve the exchange of anyons around junctions in a network of nanowires.
Recent additional research in my group has studied the natural orbitals and occupation numbers in anyonic systems.
The natural occupation numbers can be thought of as the amplitudes of orbitals when the ground state of a many-particle quantum system is approximated with single-particle orbitals.
We found that these occupation numbers decay more slowly for two-dimensional anyons than for three-dimensional electrons, establishing a greater correlation for particles in two-dimensions.
Natural orbitals and their occupation numbers for free anyons in the magnetic gauge (arXiv) with Tomasz Maciazek and Jerzy Cioslowski, Physical Review A, 2023.
Master's Dissertation: Mathematical Modelling of the Violin My dissertation for the fourth year of my integrated master's degree from Durham, on "Mathematical Modelling of the Violin". The dissertation was submitted to the Department of Mathematical Sciences in April, 2022. The dissertation covers the history of violin making, the theory of elasticity, the mechanics of elastic strings and plates and numerical solutions to partial differential equations.