A recent breakthrough in physics has been the proposal and observation of novel out of equilibrium phases of matter in many-body quantum systems, with time crystals as one prominent example. For these phases to be stable it is required that ergodicity is impeded, otherwise heat death of the system is inevitable. This theoretical project is aimed at studying a particular approach to impeding ergodicity: kinetic constraints, as first studied in classical systems.
The project will involve both numerical and analytical approaches: Numerical experiments will provide insight into the phenomenology to be studied using analytical tools, themselves supplemented by numerical approaches.
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The recent progress in exploring non-equilibrium dynamics of isolated many-body quantum systems has brought renewed attention on the dynamics and thermalisation of closed systems.
Significant effort has been devoted to studying phenomena far from equilibrium in such systems, often by driving the systems periodically–an example being the discrete time crystals recently observed in experiments. Ergodic systems eventually heat up under these conditions, complicating the observation of such phenomena. It is therefore of interest to understand how to break ergodicity in a robust, non fine-tuned way, providing access to the far from equilibrium regime where new phenomena await discovery.
While most work on ergodicity breaking over the last decade has focused on disorder-induced ergodicity breaking in many-body localised (MBL) systems, recent work has turned to ergodicity breaking in kinetically constrained systems such as appear in Rydberg atom physics. Classically, such constraints amount to forbidding certain dynamical processes; quantum mechanically they map to the vanishing of matrix elements corresponding to such transitions.
This project will help develop numerical and theoretical tools and apply them to kinetically constrained models so as to obtain their phenomenology. Based on that, we will then develop approximate analytical tools to provide further insight.
You will work in a small but active research group of four researchers, in close contact with other groups around the country.
Entry requirements for United Kingdom
Applicants should have, or expect to achieve, at least a 2:1 honours degree (or equivalent) in physics or a related subject.
Please see the programme website for international entry requirements by country.
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
HOW TO APPLY
All applications should be made online. Under programme name, select 'Mathematical Sciences'. Please quote reference number: AL/MA/2022.