Analytical models of selected stochastic processes in condensed phase systems

Abstract

This thesis is a record of the research I have carried out over the last five years to understand a selection of problems in the broad area of single-molecule physics. These problems cover four broad themes: (i) dynamically disordered Brownian motion, which deals with a new class of dynamics in which the mean square displacement of a particle scales linearly with time but the distribution of displacements is non-Gaussian, (ii) the stochastic thermodynamics of single colloids, which discusses the validity of various fluctuation theorems in two previously unexplored model systems: a harmonic oscillator acted on by a time-dependent drift, and a dual-temperature Brownian particle in an asymmetric harmonic well, (iii) the dynamics of flow-driven entangled polymers, which explores chain relaxation within a generalized Langevin equation formalism, obviating the need to invoke the widely-used but phenomenological tube model of melt relaxation, and (iv) modified diffusion in chemically active Brownian oscillators, which looks at the one-dimensional dynamics of a Brownian particle that switches at random between two different harmonic potentials as a model of the effects of chemical activity on particle motion.