Recoil of a driven tracer in a correlated medium

TL;DR

This paper investigates the recoil behavior of a driven Brownian particle in a correlated medium, revealing how the particle moves opposite to the drag after release, with dynamics depending on the medium's relaxation properties.

Contribution

It introduces a theoretical framework for understanding the recoil effect of a driven tracer in a fluctuating correlated medium, highlighting the role of medium dynamics and criticality.

Findings

Recoil occurs when the particle is released from a moving trap.

Recoil effect vanishes if the medium equilibrates instantaneously.

Final particle position reaches equilibrium algebraically over time.

Abstract

We study the stochastic dynamics of a Brownian particle after it is suddenly released from a harmonic trap moving with constant velocity through a fluctuating correlated medium, described by a scalar Gaussian field with relaxational dynamics and in contact with a thermal bath. We show that, after the release, the particle exhibits recoil, i.e., it moves in the direction opposite to the drag. As expected, this effect vanishes if the field equilibrates instantaneously. The final value of the average position of the particle is reached algebraically in time in the case of conserved dynamics of the field or for non-conserved dynamics at the critical point. Our predictions are expected to be relevant, at least qualitatively, to driven colloidal particles in liquid media close to critical points.