Research Associate (x2): Rare Events in Non-equilibrium Statistical Physics

Two postdoctoral positions are available within the Soft Matter Group in the Department of Applied Mathematics and Theoretical Physics (DAMTP), part of the Faculty of Mathematics. This follows the award of a UKRI Grant to Investigators Mike Cates, Rob Jack, and Ronojoy Adhikari.

The Project is titled Nucleation and Extinction in Non-equilibrium Statistical Field Theories. It aims to create a non-equilibrium analogue to classical nucleation theory (CNT) for statistical field theories. In CNT the nucleation rate for a transition between phases is calculable from the free energy barrier corresponding to a critical nucleus. For non-equilibrium nucleation problems, such as phase transitions in an active fluid, no free energy exists and there is no general counterpart to CNT. Other such problems include the nucleation of an invading species in a new environment and the noise-induced transition between different flow patterns in a driven fluid. A closely related problem class is when noise leads to the extinction of an otherwise stable population, gene, or behavioural trait.

Progress in large deviation theory (LDT) has created tools, such as the quasi-potential, to address non-equilibrium rare events; but these are not yet fully developed for field-theoretic models. The project aims to address a wide range of such models, via a 'four-fold path' as follows. Step 1 is to identify a handful of reduced coordinates, that can track the progress of the rare event. Good coordinates may emerge from mechanistic insight and/or machine learning. Step 2 is to calculate and compare barrier crossing rates numerically, both in the reduced coordinate space and in a 'ground truth' basis for the full dynamics, refining the reduced description as needed. Step 3 is to find the reduced quasi-potential landscape, and Step 4 is to reconstruct the full noisy dynamics of the reduced model, thereby achieving a non-equilibrium counterpart of CNT for the given problem.

The appointees will develop the analytical and numerical tools needed to pursue the four-fold path and use them to explore rare events associated with phase transitions and/or extinctions in a variety of stochastic field theories. The successful applicants will need strong familiarity with statistical field theory, at least some acquaintance with large deviation theory, or vice versa, and the ability to combine analytical and numerical skills to solve complex problems.

Duties may include developing and conducting research objectives, proposals, and projects. The role holders will be expected to plan and manage their own research and administration, with guidance if required. They may be called upon to prepare proposals and applications to external bodies for funding. They must be able to communicate material of a technical nature and build internal and external contacts. They may be asked to assist in the supervision of student projects and in the development of student research skills, and provide instruction or plan/deliver seminars relating to the research area.

Fixed-term: The funds for these posts are available for 24 months in the first instance.

We welcome applications from candidates able to take up their position on or before 1 October 2025 . A start date as early as March 2025 may be possible by mutual agreement.

The project is structured into the following four work packages. WP1: New Numerical Tools; WP2: Nucleation in Active Matter; WP3: Spatial Models; WP4: Barrier Crossing in Fluids. We are recruiting primarily to WP1 and WP2 in this call. Contract extension beyond 24 months is possible for appointees who also have skills relevant to the remaining WPs.

The University of Cambridge values diversity and is committed to equality of opportunity. The Department would particularly welcome applications from women, since women are, and have historically been, underrepresented on our research staff.

The University has a responsibility to ensure that all employees are eligible to live and work in the UK.