Dynamics of trap models

TL;DR

This paper reviews recent mathematical results on the long-time dynamics of trap models, a class of disordered media, with a focus on mean-field spin-glasses, providing a detailed analysis of their behavior.

Contribution

It offers an in-depth mathematical analysis of trap model dynamics, highlighting new insights into their long-term behavior in disordered systems.

Findings

Characterization of long-time dynamics of trap models

Mathematical descriptions of aging phenomena

Insights into mean-field spin-glass behavior

Abstract

These notes cover one of the topics of the class given in the Les Houches Summer School ``Mathematical statistical physics'' in July 2005. The lectures tried to give a summary of the recent mathematical results about the long-time behaviour of dynamics of (mean-field) spin-glasses and other disordered media. We have chosen here to restrict the scope of these notes to the dynamics of trap models only, but to cover this topic in somewhat more depth.