Persistent nonequilibrium effects in generalized Langevin dynamics of nonrelativistic and relativistic particles

TL;DR

This paper investigates persistent nonequilibrium phenomena in generalized Langevin dynamics for both nonrelativistic and relativistic particles, revealing effects like memory, ballistic diffusion, and ergodicity breaking through analytical and numerical methods.

Contribution

It provides a comprehensive analysis of nonequilibrium effects in generalized Langevin equations, including for relativistic particles, which is a novel extension.

Findings

Identification of memory effects in relativistic Brownian motion

Analytical solutions for nonrelativistic generalized Langevin equations

Numerical evidence of anomalous motion in relativistic particles

Abstract

Persistent nonequilibrium effects such as the memory of the initial state, the ballistic diffusion, and the break of the equipartition theorem and the ergodicity in Brownian motions are investigated by analytically solving the generalized Langevin equation of nonrelativistic Brownian particles with colored noise. These effects can also be observed in the Brownian motion of relativistic particles by numerically solving the generalized Langevin equation for specially chosen memory kernels. Our analyses give rise to think about the possible anomalous motion of heavy quarks in relativistic heavy-ion collisions.