Velocity fluctuations in a one dimensional Inelastic Maxwell model

TL;DR

This paper investigates velocity fluctuations and correlations in a one-dimensional Inelastic Maxwell Model, revealing divergence in moments and implications for energy fluctuations during cooling and steady states.

Contribution

It extends previous methods to analyze two-particle correlations and pair correlation functions in the Inelastic Maxwell Model, highlighting divergence issues.

Findings

Pair correlation function form in the cooling regime

Divergence of some moments of the correlation function

Implications for energy fluctuation behavior

Abstract

We consider the velocity fluctuations of a system of particles described by the Inelastic Maxwell Model. The present work extends the methods, previously employed to obtain the one-particle velocity distribution function, to the study of the two particle correlations. Results regarding both the homogeneous cooling process and the steady state driven regime are presented. In particular we obtain the form of the pair correlation function in the scaling region of the homogeneous cooling process and show that some of its moments diverge. This fact has repercussions on the behavior of the energy fluctuations of the model.