Mode-Coupling Theory (MCT) Lecture Notes

TL;DR

This paper provides a comprehensive review of mode-coupling theory for the glass transition, including derivations from microscopic and field-theoretic perspectives, and discusses its successes, failures, and recent advances.

Contribution

It offers a detailed derivation of mode-coupling equations from multiple theoretical perspectives and reviews recent developments in the field.

Findings

Derivation of mode-coupling equations from microscopic considerations.

Derivation of schematic mode-coupling equations from a field-theoretic perspective.

Discussion of the successes and limitations of mode-coupling theory.

Abstract

In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the use the Mori-Zwanzig projection operator technique. We also derive schematic mode-coupling equations of a similar form from a field-theoretic perspective. We review the successes and failures of mode-coupling theory, and discuss recent advances in the applications of the theory.