Mode-Coupling Approximations, Glass Theory and Disordered Systems

TL;DR

This paper explores the connection between mode-coupling equations, glass theory, and disordered systems, proposing extensions to lower temperatures and suggesting experiments to test key predictions about aging and time regimes.

Contribution

It establishes a theoretical link between mode-coupling approximations and spin-glass dynamics, and proposes extending the framework to include aging effects at lower temperatures.

Findings

Identifies a connection between mode-coupling equations and spin-glass models.

Suggests extending mode-coupling theory below the freezing temperature.

Proposes experiments to test the relation between short and long time dynamics.

Abstract

We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in a random potential. The physical consequences of this interrelation are underlined. It suggests to extend the mode-coupling approximation to temperatures well below the freezing temperature, in which aging effects become important. In this regime we suggest some new experiments in order to test a non-trivial prediction of the Mode-Coupling picture, which is a generalized relation between the short ($\beta$) and long ($\alpha$) time regimes.