Dynamics of a colloidal particle coupled to a Gaussian field: from a confinement-dependent to a non-linear memory

TL;DR

This paper introduces a non-linear memory model for colloidal particles in complex media, accounting for confinement effects and providing a new fluctuation-dissipation relation that aligns with experimental observations.

Contribution

It develops a novel non-linear memory framework for colloidal dynamics coupled to a Gaussian field, extending previous linear models and explaining confinement-dependent behaviors.

Findings

The model captures confinement-dependent memory effects.

A new fluctuation-dissipation relation is derived.

The approach aligns with experimental and numerical data.

Abstract

The effective dynamics of a colloidal particle immersed in a complex medium is often described in terms of an overdamped linear Langevin equation for its velocity with a memory kernel which determines the effective (time-dependent) friction and the correlations of fluctuations. Recently, it has been shown in experiments and numerical simulations that this memory may depend on the possible optical confinement the particle is subject to, suggesting that this description does not capture faithfully the actual dynamics of the colloid, even at equilibrium. Here, we propose a different approach in which we model the medium as a Gaussian field linearly coupled to the colloid. The resulting effective evolution equation of the colloidal particle features a non-linear memory term which extends previous models and which explains qualitatively the experimental and numerical evidence in the presence of confinement. This non-linear term is related to the correlations of the effective noise via a novel fluctuation-dissipation relation which we derive.