Active particles, ratchets and their field theories

Abstract

This thesis aims to address problems in active matter by employing techniques in both stochastic processes and statistical field theories. It is mainly divided into two parts: first, applications of stochastic processes to find the entropy production of var- ious exactly solvable models and solve the dynamics of a Run-and-Tumble particle in a piecewise linear potential, and second, applications of field theories to find the optimal shape for maximising currents of a Run-and-Tumble particle perturbatively and probing the particle identities using different field theories. In Chapter 1, I de- rive various methods and results from stochastic processes that are used in the rest of the thesis. In Chapter 2, I present a self-contained review of entropy production and calculate it from first principles for various exactly solvable models. In Chap- ter 3, I solve the steady-state dynamics of a Run-and-Tumble particle in a piece- wise linear ratchet and calculate various other quantities such as particle current, entropy production and mean first passage time. In Chapter 4, I derive and present Doi-Peliti field theory and response field theory which are used in the rest of the the- sis. In Chapter 5, I present a method of solving the probability distribution perturba- tively and finding the optimal shape of the potential that maximises the probability current for a Run-and-Tumble particle using Doi-Peliti field theory. In Chapter 6, I identify the mechanism where particle entity is enforced in the context of the Doi- Peliti field theory of a diffusive particle and the response field theory that is derived from Dean’s equation.