Power-law Decay and the Ergodic-Nonergodic Transition in Simple Fluids

TL;DR

This paper extends the mathematical framework of mode coupling theory to the Fundamental Theory of Statistical Particle Dynamics, enabling calculation of power-law decay exponents in dense simple fluids using a second-order approximation.

Contribution

It demonstrates how to adapt MCT analysis techniques within the systematic framework of the Fundamental Theory, specifically for hard-sphere fluids with Percus-Yevick statics.

Findings

Power-law decay exponents can be computed in the second-order approximation.

The mathematical machinery of MCT is applicable within the Fundamental Theory framework.

Analysis reveals the ergodic-nonergodic transition in simple fluids.

Abstract

It is well known that mode coupling theory (MCT) leads to a two step power-law time decay in dense simple fluids. We show that much of the mathematical machinery used in the MCT analysis can be taken over to the analysis of the systematic theory developed in the Fundamental Theory of Statistical Particle Dynamics (arXiv:0905.4904). We show how the power-law exponents can be computed in the second-order approximation where we treat hard-sphere fluids with statics described by the Percus-Yevick solution.