Dynamical large deviations and phase separation in systems of interacting particles
Lead Research Organisation:
University of Cambridge
Department Name: Applied Maths and Theoretical Physics
Abstract
We apply large deviation theory to dynamical fluctuations in interacting particle systems. Large deviation theory describes the probabilities of rare events: we focus here on events in which a system does not behave ergodically, over a long time period. Recent work has established that such events can be accompanied by the formation of a macroscopic cluster of particles: that is, phase separation. The theoretical status of this phase coexistence remains mysterious: it seems to violate equilibrium laws such as equality of pressure (and chemical potential) between the two phases. We seek to understand the role of pressure and chemical potential in this state. There are also possible connections with motility-induced phase separation in active matter, which we will investigate.
Organisations
People |
ORCID iD |
| Robert Jack (Primary Supervisor) | |
| Jakub Dolezal (Student) |
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/N509620/1 | 01/10/2016 | 30/09/2022 | |||
| 1936378 | Studentship | EP/N509620/1 | 01/10/2017 | 31/07/2021 | Jakub Dolezal |
| Description | We have investigated the fat tail in the probability distribution of the global activity in a system of diffusing particles. We have classified several distinct regimes of this probability distribution, explored them numerically and analytically and explained their main properties. This is one of the two foci of the paper associated with the award. In the course of the above research we have used novel methods of sampling rare events. These were the second part of the above mentioned paper. The tails of the distribution were simulated more efficiently with importance sampling by adding control forces. This improved the efficiency of our simulations and allowed us to investigate system sizes and regimes we previously wouldn't have been able to. We explored by how much simple control forces improve our simulations and how to determine the best ones to use. The findings about using control forces are transferable to the sampling of rare events in other systems. On a more personal level I have developed my skills both as a physicist and a programmer and acquired specialist knowledge about large deviations. We are still working on understanding the role that pressure and chemical potential play in these systems which was one of the main objectives of the award. We have begun investigating it analytically and with simulations but we have not yet obtained enough results to publish them. During the project we noticed that being in the tails of the probability distribution of a local activity impacts the system globally in a way that scales with system size. This is a rather novel finding that we are still looking into. |
| Exploitation Route | The findings regarding the diffusive system and the large deviations of its activity could inspire further research within the physics community. Our discussion with Prof. Juan P. Garrahan's group is a specific impact our paper has already had. They were fairly interested in our research both when it comes to the physics as well as the methods. Importance sampling has already been used to study the climate, protein folding or glass formation among others. Our findings about using control forces to improve simulations could be used in these same fields. |
| Sectors | Environment |