Interactions, correlations and collective behaviour in non-equilibrium systems
File(s)
Author(s)
Garcia Millan, Rosalba
Type
Thesis
Abstract
Non-equilibrium systems, which usually involve a large number of interacting particles, are ubiquitous in nature and society. Interactions, such as volume exclusion or branching, induce correlations in the system and often translate into emergent collec- tive behaviour at macroscopic scales. This is the case, for instance, in active matter, where particles are subject to local non-thermal forces that are transformed into mechanical work. Establishing the relationship between macroscopic patterns and microscopic dynamics analytically is a challenge that has motivated different approaches in the community.
In this thesis I have focused on some statistical properties with an emphasis on correlations, both spatial and temporal, of six different non-equilibrium particle systems: the Oslo rice pile model, branching processes and applications, the voter model, and run-and-tumble motion. The first three systems display critical phenomena and the last one is an instance of active motility.
The approaches that I have followed are, on the one hand, one-to-one mappings between different, known, stochastic processes and, on the other hand, the Doi-Peliti field theory formalism. The point in common between both approaches is the ability to retain the particle entity, which proves essential when tackling observables that strongly depend on the microscopic dynamics of the system, such as correlation functions. However, the field-theoretic approach is much more systematic, as it becomes apparent in the applicability of this route to different kinds of reaction-diffusion particle systems.
In this thesis I have focused on some statistical properties with an emphasis on correlations, both spatial and temporal, of six different non-equilibrium particle systems: the Oslo rice pile model, branching processes and applications, the voter model, and run-and-tumble motion. The first three systems display critical phenomena and the last one is an instance of active motility.
The approaches that I have followed are, on the one hand, one-to-one mappings between different, known, stochastic processes and, on the other hand, the Doi-Peliti field theory formalism. The point in common between both approaches is the ability to retain the particle entity, which proves essential when tackling observables that strongly depend on the microscopic dynamics of the system, such as correlation functions. However, the field-theoretic approach is much more systematic, as it becomes apparent in the applicability of this route to different kinds of reaction-diffusion particle systems.
Version
Open Access
Date Issued
2020-04
Date Awarded
2020-08
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Pruessner, Gunnar
Sponsor
Department of Mathematics
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)