A study of non-linear Langevin dynamics under non-Gaussian noise with quartic cumulant

TL;DR

This paper investigates non-linear Langevin dynamics with non-Gaussian noise, revealing how physical parameters relate to Langevin parameters through renormalisation, and analyzing thermalization behavior via velocity correlation functions.

Contribution

It introduces a path-integral approach to connect Langevin parameters with physical parameters and studies the effects of non-Gaussian noise on thermalization and correlation functions.

Findings

Velocity two-point function saturates to bath temperature.

Velocity four-point function matches thermal predictions when non-linear FDR holds.

Violation of non-linear FDR prevents full thermalization, leading to a steady state.

Abstract

We consider a non-linear Langevin equation in presence of non-Gaussian noise originating from non-linear bath. We claim, the parameters in the Langevin equation are not physical. The physical parameters are obtained from a path-integral description of the system, where the Langevin parameters are related to the physical parameters by renormalisation flow equations. Then we compute both numerically and analytically the velocity two point function and show that it saturates to the bath temperature even in presence of non-linearity. We also find the velocity four point function numerically and show that it saturates to the analytically evaluated thermal velocity four point function when the non-linear FDR [1] is satisfied. When the non-linear FDR, which is a manifestation of time reversibility of thermal bath, is violated then the system does not seem to thermalise. Rather, its velocity four point function settles to a steady state.