Universal power law tails of time correlation functions

TL;DR

This paper derives universal power law tails for time correlation functions in various systems using hydrodynamic modes, revealing common long-time behaviors across classical fluids and Lorentz gases.

Contribution

It introduces a unifying theoretical framework for power law tails in time correlation functions applicable to diverse systems beyond classical fluids.

Findings

Power law tails decay as t^{-1-d/2} in dense classical fluids.

Universal behavior of correlation functions derived from hydrodynamic modes.

Long-time tails observed in both single and multi-particle correlation functions.

Abstract

The universal power law tails of single particle and multi-particle time correlation functions are derived from a unifying point of view, solely using the hydrodynamic modes of the system. The theory applies to general correlation functions, and to systems more general than classical fluids. Moreover it is argued that the collisional transfer part of the stress-stress correlation function in dense classical fluids has the same long time tail $\sim t^{-1-d/2}$ as the velocity autocorrelation function in Lorentz gases.