Time correlations and persistence probability of a Brownian particle in a shear flow

TL;DR

This paper investigates the time correlations and persistence probabilities of Brownian particles in shear flow, revealing distinct diffusive and superdiffusive behaviors, and extends analysis to particle chains with harmonic and bending interactions.

Contribution

It provides new analytical results for two-time correlation functions and persistence probabilities of Brownian particles under shear flow, including confined particles and chains.

Findings

Diffusive and superdiffusive regimes identified for free particles

Plateau in mean-square-displacement for confined particles

Persistence probability constructed from correlation functions

Abstract

In this article, results have been presented for the two-time correlation functions for a free and a harmonically confined Brownian particle in a simple shear flow. For a free Brownian particle, the motion along the direction of shear exhibit two distinct dynamics, with the mean-square-displacement being diffusive at short times while at late times scales as $t^3$. In contrast the cross-correlation $\la x(t) y(t) \ra $ scales quadratically for all times. In the case of a harmonically trapped Brownian particle, the mean-square-displacement exhibits a plateau determined by the strength of the confinement and the shear. Further, the analysis is extended to a chain of Brownian particles interacting via a harmonic and a bending potential. Finally, the persistence probability is constructed from the two-time correlation functions.