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Dr Andrew Ho - Condensed Matter Theory
Non-equilibrium dynamics and thermalisation in simple quantum systems
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- Thermalisation in small quantum systems
This is a theoretical project involving numerical computation and some analytical calculation. The question is this: when a small quantum system is coupled to a larger quantum system, how does the small quantum system thermalise (or not!) after an initial perturbation that takes the system far from equilibrium? As the project involves tools, concepts from statistical physics, quantum mechanics and numerical simulations, you need to be comfortable and proficient in all these. Reference: Genway et al., Physical Review Letters 105, 260402 (2010); Physical Review Letters 111, 130408 (2013).
- Many-body Localisation
Also a theoretical project involving numerical computation. Recent theoretical (and maybe also experimental) research has uncovered a class of quantum many-body systems where a system can never relax to thermal equilibrium: this involves a competition between disorder and strong interaction between the quantum particles. A key question is this: as we change the strength of the interaction, how does the system go from thermalising, to non-thermalising (said to be Many-body Localised)? Again the project involves tools, concepts from statistical physics, quantum mechanics and numerical simulations, so you need to be comfortable and proficient in all these. Reference: Nandkishore Annu. Rev. Condens. Matter Phys. 6:15-38 (2015).
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- Quantum time evolution and thermalisation in a single quantum spin-1/2 coupled to a larger quantum bath
This is a theoretical project involving mainly computer simulation of a small number of spin-1/2’s coupled with neighbours via an exchange coupling. The questions to be addressed can involve one or more of: what conditions are needed for some particular initial state to achieve thermalisation in this quantum system + bath set up? What is the timescale and form of the relaxation to equilibrium? If the system does not relax to equilibrium to eg. A Boltzmann distribution, what does it do? The project builds on material from Quantum mechanics (especially spin-1/2), PH2610 Classical and Statistical Thermodynamics. Some exposure to one of Mathematica, Python, C++, etc is expected. Reference: Genway et al., Physical Review Letters 105, 260402 (2010); Physical Review Letters 111, 130408 (2013).
- Epidemic modelling via the physics of the kinetics of Crystallization
In non-equilibrium statistical mechanics, it is well known that quite different phenomenon like forest fires, epidemic spreading, and crystallization, etc can have surprisingly similar modelling in terms of coupled differential equations of "particles" or "agents". In this computational project, we will try to see if Covid-19 infection in various countries (at least for the first wave) could be modelled using some simple physical models. Prerequisites: some exposure to one of Mathematica, Python, C++, etc.
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Dr Gregoire Ithier - Condensed Matter Quantum Devices
- Quantum dynamics of interacting fermions
This project aims at simulating numerically the quantum dynamics of a system of strongly interacting fermions, in order to study the new dynamical states of matter which have been observed in recent experiments. The project is both theoretical and computer based. The student will become familiar with the numerical technique of exact diagonalization and matrix manipulation in python.
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Both projects require writing a computer program from scratch. Therefore, computer-programming skills are a pre-requisite for both projects. |
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--  Pedro Teixeira Dias - 07 Jun 2021 |
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