Crossover in the Slow Decay of Dynamic Correlations in the Lorentz Model

TL;DR

This paper investigates the long-time behavior of transport coefficients in a Lorentz model, revealing complex decay patterns influenced by percolation and trapping effects through Molecular Dynamics simulations.

Contribution

It provides new insights into the interplay of critical relaxation, hydrodynamic anomalies, and trapping in the decay of correlations in heterogeneous media.

Findings

Velocity auto-correlation exhibits power-law decay influenced by percolation.

In 2D, trapping causes a -3 power law anomaly instead of -2.

Burnett coefficient diverges logarithmically in dilute limit, with stronger divergences at finite density.

Abstract

The long-time behavior of transport coefficients in a model for spatially heterogeneous media in two and three dimensions is investigated by Molecular Dynamics simulations. The behavior of the velocity auto-correlation function is rationalized in terms of a competition of the critical relaxation due to the underlying percolation transition and the hydrodynamic power-law anomalies. In two dimensions and in the absence of a diffusive mode, another power law anomaly due to trapping is found with an exponent -3 instead of -2. Further, the logarithmic divergence of the Burnett coefficient is corroborated in the dilute limit; at finite density, however, it is dominated by stronger divergences.