# A note on the violation of the Einstein relation in a driven moderately dense granular gas - Condensed Matter > Statistical Mechanics

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Abstract: The Einstein relation for a driven moderately dense granular gas in$d$-dimensions is analyzed in the context of the Enskog kinetic equation. TheEnskog equation neglects velocity correlations but retains spatial correlationsarising from volume exclusion effects. As expected, there is a breakdown of theEinstein relation $\epsilon=D-T 0\mu eq 1$ relating diffusion $D$ andmobility $\mu$, $T 0$ being the temperature of the impurity. The kinetic theoryresults also show that the violation of the Einstein relation is only due tothe strong non-Maxwellian behavior of the reference state of the impurityparticles. The deviation of $\epsilon$ from unity becomes more significant asthe solid volume fraction and the inelasticity increase, especially when thesystem is driven by the action of a Gaussian thermostat. This conclusionqualitatively agrees with some recent simulations of dense gases Puglisi {\emet al.}, 2007 {\em J. Stat. Mech.} P08016, although the deviations observed incomputer simulations are more important than those obtained here from theEnskog kinetic theory. Possible reasons for the quantitative discrepanciesbetween theory and simulations are discussed.

Author: ** Vicente Garzo**

Source: https://arxiv.org/