Power law tails of time correlations in a mesoscopic fluid model

TL;DR

This study uses computer simulations to verify the predicted power law decay in energy autocorrelation functions in mesoscopic fluids, confirming theoretical predictions across different dimensions and system sizes.

Contribution

It provides the first comprehensive simulation validation of mode coupling theory predictions for power law tails in mesoscopic fluid models.

Findings

Power law tail ~ t^{-d/2} matches simulation results

Finite size effects are well-accounted for in the theory

Agreement observed in both 1D and 2D systems

Abstract

In a quenched mesoscopic fluid, modelling transport processes at high densities, we perform computer simulations of the single particle energy autocorrelation function C_e(t), which is essentially a return probability. This is done to test the predictions for power law tails, obtained from mode coupling theory. We study both off and on-lattice systems in one- and two-dimensions. The predicted long time tail ~ t^{-d/2} is in excellent agreement with the results of computer simulations. We also account for finite size effects, such that smaller systems are fully covered by the present theory as well.