# Projects

The Level 3 computer project will allow you to investigate an exciting physics problem in the same way many researchers investigate new problems in their research work. The projects have been specially designed to cover some of the main areas of research inside the department. Feel free to have a look at the projects that have previously been available below.

*Please note that it may not always be possible to offer all of these projects in any particular year.*

## Astronomy & Astrophysics

**The Equation of State of White Dwarves and Neutron Stars:**This project will calculate models for the interior structures of white dwarfs and neutron stars and use them to derive the global physical properties under a variety of assumptions about the equation of state of degenerate matter. The physics involved includes thermodynamics, quantum statistics, nuclear physics and general relativity. The computational methods require solving coupled differential equations in both the Newtonian and general relativistic limits which can be extended to include nuclear forces and modification to GR.**Rockets, Asteroids and the Restricted 3 Body Problem:**This project will develop accurate numerical solutions to the gravitational restricted 3-body problem: the motion of a light object in the gravitational field two massive bodies. Although a deceptively simple problem, the project requires that orbits are integrated with high accuracy. This approach can be used to study the motion of rockets, asteroids, planets and even colliding galaxies, providing powerful insight into many astrophysical phenomenon.**The Black Hole Accretion Disk Spectrum:**This project studies the emission spectrum of the accretion disk around a black hole. By constructing a simple model for the emission spectrum it is possible to interpret data cycles in the hardness-intensity diagram of galactic black holes and to understand the different phases of black hole accretion disks. Alternatively, by incorporating relativistic effects, it is possible to investigate whether black holes spin.**Supernova Cosmology:**Because supernovae have a well-defined peak luminosity, they offer a powerful means of measuring the geometry and expansion rate of the Universe. This project will develop the tools needed to deduce the expansion history of the universe from recent data sets.**Gravitational collapse:**This project will develop a simple code for simulating systems of many interacting gravitational particles. The simulation code will need to be fast so that large systems can be investigated. Applications include the collapse of a galaxy cluster, the development of mass segregation in a globular cluster or the growth of structure in the Universe.

## Atomic and Optical Physics

**Solitons:**Solitons are localised waves that arise throughout nature as a result of a non-linearity in the wave equation. One of the most exciting examples is the matter wave soliton formed from an ultra-cold atomic Bose Einstein condensate. These macroscopic superpositions of de Broglie waves probe the boundary of wave-particle duality is an extreme way. This project will involve numerical simulation of soliton collisions by solving the non-linear Schrodinger equation.**Fourier Optics:**The propagation of light is described by the solution of Maxwell's equations which in many cases can be found using Fourier methods. Some particularly interesting examples include the propagation in the shadow of an object leading to superluminal effects, and the Talbot effect. In this project the angular spectrum method will be used to study superluminal phase propagation associated with the spot of Arago.**Light-matter interactions:**Atoms makes the most accurate sensors available as illustrated for example by the atomic clock. But to exploit this precision we need to need to understand how atom respond to electric and magnetic fields. In this project we will calculate the energy level and hence the optical transition frequencies of real atoms in the presence of electric and magnetic fields using matrix methods.**Quantum computing:**The miniaturisation of computer processors motivates thinking about using single quantum objects (qubits) as processing units. The dynamics of qubits are described by the optical Bloch equations. In this project we will explore the dynamics of a qubits including state preparation by solving the optical Bloch equations.

## Condensed/Soft Matter Physics

**MC simulation of colloidal fluids:**Soft matter physics is often characterised by the importance of entropy or thermal fluctuations. This is exemplified by the so-called hard sphere model, consisting of impenetrable (colloidal) particles which otherwise do not interact. It is one of the first ever systems studied using computer simulations, among others, as a simple model for liquid and for answering the (then) long-standing debate of whether entropy alone can drive a liquid to solid phase transition. In this project, the student will develop a Monte Carlo code to explore the phase behaviour of this deceptively complex system.**The Band Structure of Silicon and Other Crystals:**This project will develop a code to model the band structures of simple crystals such as Silicon and Germainium. The band structures that emerge from the calculations can be compared against experimental data for the conduction band gap, and for the heat capacity. The structure calculations can be readily extended to a wide variety of materials.**Simulation of Semi-Conductor Barriers:**This project studies the propagation of electrons through a series of one-dimensional potential wells, exploring phenomena such as resonant transmission. The simulation can be compared to experimental systems and used to better understand a wide variety of quantum phenomena.**Phase transition:**Phase transitions are of crucial importance in modern physics. This project will develop a simple model for the interaction of magnetic atoms locked into a crystal. By randomly flipping the orientation of atoms relative to their neighbours, the project will investigate how large scale organized structures emerge at sufficiently low temperatures. The project will investigate a range of critical phenomena and hysteresis behavior.

## Particle Physics

**The Feynman Path Integral:**Feynman suggested a powerful approach to quantum mechanical problems. He showed the quantum mechanics can be re-formulated as an integral over the possible paths connecting two states. This project will develop a simple code for solving such problems, and apply the method to simple problems in order to gain a deeper understanding of the quantum mechanics.**Probing the Structure of Particles with Resonant Scattering:**This project will develop a code for the quantum mechanical scattering of particles off a potential. Scattering experiments allow us to probe the structure of nuclei and sub-atomic particles, with resonances in the scattering being used to identify excited states of the target particle. Accurately modelling is fundamental to understanding data obtained at the LHC, and the project will explore diverse applications of the simulation codes.**Quarkonium and the Nature of the Strong Force:**Starting from a simple model of the hydrogen atom, the project will explore the nature of sub-atomic interactions. In particular, it will focus on the bound states expected for systems consisting of two quarks, providing insight into the nature of the strong force.**3-Particle Systems in Quantum Mechanics:**This project will investigate Hylleraas’s method, which is based on the variational principle, for solving quantum mechanical systems of multiple particles, such as the Helium atom. The method allows the energy spectra of molecules and multi-electron atoms to be computed from first principles, providing stringent tests of quantum theory.