A classical long-time tail in a driven granular fluid

TL;DR

This paper develops a mode-coupling theory to explain the algebraic decay of the velocity autocorrelation function in a driven granular fluid, confirming simulation predictions and revealing the role of transverse current coupling.

Contribution

It introduces a theoretical framework for the long-time tail in driven granular fluids, extending understanding of non-equilibrium dynamics in such systems.

Findings

Velocity autocorrelation function decays as t^{-3/2} when momentum is conserved.

The slow decay results from coupling to transverse currents.

The theory confirms previous simulation conjectures.

Abstract

I derive a mode-coupling theory for the velocity autocorrelation function, \psi(t), in a fluid of randomly driven inelastic hard spheres far from equilibrium. With this, I confirm a conjecture from simulations that the velocity autocorrelation function decays algebraically, \psi(t) ~ t^{-3/2}, if momentum is conserved. I show that the slow decay is due to the coupling to transverse currents.