Perturbation spreading in many-particle systems: a random walk approach

TL;DR

This paper models the spread of localized perturbations in many-particle systems using a continuous-time random walk framework, linking microscopic dynamics to macroscopic diffusion profiles.

Contribution

It introduces a random walk approach to describe perturbation propagation in ergodic many-particle systems, connecting physical parameters to diffusion behavior.

Findings

Perturbation profiles match Levy walk diffusion profiles.

Parameters of the random walk relate to physical system parameters.

Validates the approach with hard-point gas and Fermi-Pasta-Ulam chain.

Abstract

The propagation of an initially localized perturbation via an interacting many-particle Hamiltonian dynamics is investigated. We argue that the propagation of the perturbation can be captured by the use of a continuous-time random walk where a single particle is traveling through an active, fluctuating medium. Employing two archetype ergodic many-particle systems, namely (i) a hard-point gas composed of two unequal masses and (ii) a Fermi-Pasta-Ulam chain we demonstrate that the corresponding perturbation profiles coincide with the diffusion profiles of the single-particle L\'{e}vy walk approach. The parameters of the random walk can be related through elementary algebraic expressions to the physical parameters of the corresponding test many-body systems.