The modified Langevin description for probes in a nonlinear medium

TL;DR

This paper derives a nonlinear Langevin equation for probes in a medium where strong disturbances alter the bath's response, introducing new terms and time-scales relevant for complex media like visco-elastic substances.

Contribution

It introduces a second-order response-based derivation of a nonlinear Langevin equation accounting for bath perturbations in non-equilibrium conditions.

Findings

New nonlinear Langevin equation with non-dissipative terms

Identification of a novel time-scale linked to bath activity

Application to colloid motion in visco-elastic media

Abstract

When the motion of a probe strongly disturbs the thermal equilibrium of the solvent or bath, the nonlinear response of the latter must enter the probe's effective evolution equation. We derive that induced stochastic dynamics using second order response around the bath thermal equilibrium. We discuss the nature of the new term in the evolution equation which is not longer purely dissipative, and the appearance of a novel time-scale for the probe related to changes in the dynamical activity of the bath. A major application for the obtained nonlinear generalized Langevin equation is in the study of colloid motion in a visco-elastic medium.