A resetting particle embedded in a viscoelastic bath

TL;DR

This paper investigates the dynamics of a colloidal particle in a viscoelastic bath with stochastic resetting, extending the generalized Langevin equation to include resetting effects, and analyzes how memory influences the particle's behavior.

Contribution

We extend the renewal formalism to incorporate resetting in systems governed by the Generalized Langevin Equation, providing analytical expressions for position variance and correlation functions.

Findings

Identification of timescales and transient plateaus in the particle's dynamics.

Resetting influences the relaxation and steady-state behavior of the system.

Numerical simulations confirm the analytical results with high accuracy.

Abstract

We examine the behavior of a colloidal particle immersed in a viscoelastic bath undergoing stochastic resetting at a rate $r$. Microscopic probes suspended in viscoelastic environment do not follow the classical theory of Brownian motion. This is primarily because the memory from successive collisions between the medium particles and the probes does not necessarily decay instantly as opposed to the classical Langevin equation. To treat such a system one needs to incorporate the memory effects to the Langevin equation. The resulting equation formulated by Kubo, known as the Generalized Langevin equation (GLE), has been instrumental to describe the transport of particles in inhomogeneous or viscoelastic environments. The purpose of this work, henceforth, is to study the behavior of such a colloidal particle governed by the GLE under resetting dynamics. To this end, we extend the renewal formalism to compute the general expression for the position variance and the correlation function of the resetting particle driven by the environmental memory. These generic results are then illustrated for the prototypical example of the Jeffreys viscoelastic fluid model. In particular, we identify various timescales and intermittent plateaus in the transient phase before the system relaxes to the steady state; and further discuss the effect of resetting pertaining to these behaviors. Our results are supported by numerical simulations showing an excellent agreement.