Mode-coupling theory for multiple-time correlation functions of tagged particle densities and dynamical filters designed for glassy systems

TL;DR

This paper extends mode-coupling theory to include tagged particle densities for analyzing dynamical heterogeneities in glassy systems, providing exact expressions and testing them against simulations.

Contribution

It introduces a formalism for higher-order correlation functions involving tagged particles, applicable to glassy dynamics, and validates the theory with simulation data.

Findings

Derived mode-coupling expressions for relaxation indicators

Successfully tested theoretical predictions against hard sphere fluid simulations

Provided a framework for analyzing dynamical heterogeneities in glasses

Abstract

The theoretical framework for higher-order correlation functions involving multiple times and multiple points in a classical, many-body system developed by Van Zon and Schofield [Phys. Rev. E 65, 011106 (2002)] is extended here to include tagged particle densities. Such densities have found an intriguing application as proposed measures of dynamical heterogeneities in structural glasses. The theoretical formalism is based upon projection operator techniques which are used to isolate the slow time evolution of dynamical variables by expanding the slowly-evolving component of arbitrary variables in an infinite basis composed of the products of slow variables of the system. The resulting formally exact mode-coupling expressions for multiple-point and multiple-time correlation functions are made tractable by applying the so-called N-ordering method. This theory is used to derive for moderate densities the leading mode coupling expressions for indicators of relaxation type and domain relaxation, which use dynamical filters that lead to multiple-time correlations of a tagged particle density. The mode coupling expressions for higher order correlation functions are also succesfully tested against simulations of a hard sphere fluid at relatively low density.