Intermediate dynamics between Newton and Langevin

TL;DR

This paper explores an intermediate regime of Brownian dynamics described by the generalized Langevin equation, revealing anomalous behaviors like ballistic diffusion and examining effects of initial correlations on long-term dynamics.

Contribution

It introduces a unified framework for dynamics between Newton and Langevin formalisms, highlighting anomalous behaviors and the impact of initial correlations in non-Markovian systems.

Findings

Identification of ballistic diffusion in non-Markovian Brownian motion

Demonstration of accelerated transport due to zero-frequency friction

Analysis of initial correlation effects on long-time system behavior

Abstract

A dynamics between Newton and Langevin formalisms is elucidated within the framework of the generalized Langevin equation. For thermal noise yielding a vanishing zero-frequency friction the corresponding non-Markovian Brownian dynamics exhibits anomalous behavior which is characterized by ballistic diffusion and accelerated transport. We also investigate the role of a possible initial correlation between the system degrees of freedom and the heat-bath degrees of freedom for the asymptotic long-time behavior of the system dynamics. As two test beds we investigate (i) the anomalous energy relaxation of free non-Markovian Brownian motion that is driven by a harmonic velocity noise and (ii) the phenomenon of a net directed acceleration in noise-induced transport of an inertial rocking Brownian motor.