Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory

TL;DR

This paper analyzes the asymptotic behavior near a localization transition in glassy systems using mode-coupling theory, providing new insights into dynamic correlation functions and the effects of infrared cutoffs.

Contribution

It derives asymptotic results for key dynamic quantities near the transition and discusses the impact of infrared cutoffs within mode-coupling theory.

Findings

Asymptotic expressions for the order parameter and correlation functions

Analysis of mean-squared displacement near transition

Discussion of infrared cutoff effects on dynamics

Abstract

We discuss the dynamic behavior of a tagged particle close to a classical localization transition in the framework of the mode-coupling theory of the glass transition. Asymptotic results are derived for the order parameter as well as the dynamic correlation functions and the mean-squared displacement close to the transition. The influence of an infrared cutoff is discussed.