Non-equilibrium dynamics and turbulence in disordered Bose gas

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The existence of Bose Einstein Condensate (BEC) was originally predicted by Satyendra Nath Bose, and was later developed theoretically by Albert Einstein. In gases - which occupy the majority of the universe - billiard ball like collisions between particles dominate the governing dynamics. At very low but finite temperatures, it was predicted that a class of particles called bosons would fall into their lowest energy levels. Here the bosons cease to behave like individual particles. Rather than bouncing off each other, the particles enter the same quantum state, and the millions of bosons present are behaving as one, single, giant atom. In 1995, Cornell and Wieman reduced 2000 rubidium atoms to less than 100 billionths of a degree above absolute zero. This breakthrough lead to huge interest in BEC experiments and, in 2001, Cornell, Ketterle and Wieman receives a Nobel prize for their studies on BEC. Presently, around the globe, there are hundreds of novel experiments taking place, unearthing a plethora of results in this rich and diverse field.To this day, BECs remain a very active area of research because they are highly experimentally controllable, have widespread potential applications from interferometry and quantum computing to understanding the behaviour of Neutron stars, and are an exciting testbed for quantum mechanics. A remarkable property of weakly interacting BECs is that they lack any viscous effects, meaning that these fluids can flow without losing kinetic energy. This has led to BEC gases being dubbed "superfluids". Forcing a superfluid to rotate leads to the formation of multiple quantum vortices, where a regular, ordered vortex lattice is the ground state of the rotating BEC. Large systems have many vortices, and at low temperatures it becomes energetically more favourable for vortices to exist in tightly bound vortex anti-vortex pairs, creating long range order in the system. At high temperature, vortex pairs unbind, resulting in the destruction of long-range-order. This transition, known as the Berezinskii-Kosterlitz-Thouless (BKT) transition, describes a critical temperature at which the system sharply changes from bound vortex pairs to unbound vortices. This is in stark contrast to the smooth transition seen in 3D. Importantly, these results on the BKT transition apply only to a uniform 2D BEC, and do not necessarily apply to the case of a trapped, rotating system, which is a more complicated problem as the ground state is a vortex lattice. We will apply numerical techniques to realise novel simulations of this problem, in the limit of very large systems, in order to determine the nature of a BKT analogue in a rotating frame of reference.On completion of the project on BKT transitions in a rotating frame of reference, we will then move to a project on non-equilibrium vortex dynamics. The aim of this will be to develop novel theoretical models for vortex dynamics of cold BECs described by a point-vortex model to study a hot BEC with many sound waves. In looking at the behaviour of a hot BEC in a disordered potential, we aim to find an improved point vortex model, e.g., a point vortex model with stochastic noise terms. The link between disorder and interactions between bosons in a disordered potential is an interesting theoretical challenge, and will lead to a fascinating array of results in many-body physics. The theoretical techniques and numerical codes developed in looking at this problem will then be used to study the transition to turbulence in flow through point-like disorder potentials.