Violation of the Einstein relation in Granular Fluids: the role of correlations

TL;DR

This paper investigates how correlations in driven granular gases affect the Einstein relation, showing that strong velocity-density correlations at high densities and inelasticities lead to violations of the proportionality between response and fluctuations.

Contribution

It reveals that velocity-density correlations cause violations of the Einstein relation in granular fluids under certain conditions, despite the fluctuation-dissipation relation still holding.

Findings

Weak violations occur when velocity statistics are non-Gaussian but correlations are absent.

Strong correlations at high densities and inelasticities break the proportionality between response and velocity autocorrelation.

The fluctuation-dissipation relation remains valid even when the Einstein relation is violated.

Abstract

We study the linear response in different models of driven granular gases. In some situations, even if the the velocity statistics can be strongly non-Gaussian, we do not observe appreciable violations of the Einstein formula for diffusion versus mobility. The situation changes when strong correlations between velocities and density are present: in this case, although a form of fluctuation-dissipation relation holds, the differential velocity response of a particle and its velocity self-correlation are no more proportional. This happens at high densities and strong inelasticities, but still in the fluid-like (and ergodic) regime.