Classical Open Systems coupled to Nonlinear Baths: Noise Spectrum and Dynamical Correlations

TL;DR

This paper investigates how nonlinear thermal baths influence classical open system dynamics, focusing on noise spectra, correlations, and nonequilibrium effects using perturbative methods and specific bath models.

Contribution

It provides a detailed analysis of noise spectra and correlations in classical systems coupled to nonlinear baths, including super-Ohmic corrections and out-of-equilibrium dynamics.

Findings

Super-Ohmic corrections to the linear Ohmic spectrum identified

Velocity correlations under nonlinear baths characterized

Out-of-equilibrium correlations evaluated after quenched initial conditions

Abstract

Open system dynamics in a classical setting is microscopically governed by the structure of the thermal environment which influences the dynamics of the probe particle (free or in an external potential). Nonlinear baths have recently been shown to impart interesting nonequilibrium correlations in the dissipative dynamics affecting Generalised Langevin Equations and the Fluctuation Dissipation Relations. In the following work, we investigate some aspects of nonlinear baths with rigour relying on perturbative expansions to deal with nonlinear equations. Firstly, the question of noise spectrum emerging from such nonlinearities are addressed and the Markovian limit is explored; super-Ohmic corrections to the linear Ohmic spectrum is deduced. Velocity correlations of a probe system under such approximations are studied in detail. In a second part to the paper, a quenched initial thermal bath is modelled via nonlinearities and Louivillean evolution is applied to evaluate subsequent correlations out of equilibrium. In all these problems, weak system-bath coupling is assumed and quartic baths are used for specific calculations.