Long-Time Behavior of Velocity Autocorrelation Function for Interacting Particles in a Two-Dimensional Disordered System

TL;DR

This study uses molecular dynamics simulations to analyze how the velocity autocorrelation function (VACF) behaves over time in a two-dimensional disordered system with interactions and randomness, revealing a crossover from positive to negative tail behavior as disorder increases.

Contribution

It demonstrates the crossover in VACF tail behavior from positive to negative in a 2D disordered system with interactions, and explores the effects of nonequilibrium conditions.

Findings

VACF exhibits a crossover from t^{-1} to -t^{-2} tail with increasing disorder.

Negative tail persists even when particle and impurity densities are comparable.

VACF behavior in nonlinear response regime differs significantly from equilibrium and linear response regimes.

Abstract

The long-time behavior of the velocity autocorrelation function (VACF) is investigated by the molecular dynamics simulation of a two-dimensional system which has both a many-body interaction and a random potential. With strengthening the random potential by increasing the density of impurities, a crossover behavior of the VACF is observed from a positive tail, which is proportional to t^{-1}, to a negative tail, proportional to -t^{-2}. The latter tail exists even when the density of particles is the same order as the density of impurities. The behavior of the VACF in a nonequilibrium steady state is also studied. In the linear response regime the behavior is similar to that in the equilibrium state, whereas it changes drastically in the nonlinear response regime.