Cooperativity Beyond Caging: Generalized Mode Coupling Theory

TL;DR

This paper extends mode coupling theory by explicitly including higher order correlations, which delays the glass transition and restores ergodicity, providing a more accurate description of glassy dynamics.

Contribution

It introduces a generalized mode coupling theory that systematically incorporates higher order correlations, improving upon traditional MCT limitations.

Findings

Higher order correlations delay the transition to glassy states.

Including these correlations restores ergodicity in the model.

Relaxation times grow exponentially rather than diverge power-law.

Abstract

The validity of mode coupling theory (MCT) is restricted by an uncontrolled factorization approximation of density correlations. The factorization can be delayed and ultimately avoided, however, by explicitly including higher order correlations. We explore this approach within a microscopically motivated schematic model. Analytic tractability allows us to discuss in great detail the impact of factorization at arbitrary order, including the limit of avoided factorization. Our results indicate a coherent picture for the capabilities as well as limitations of MCT. Moreover, including higher order correlations systematically defers the transition and ultimately restores ergodicity. Power-law divergence of the relaxation time is then replaced by continuous but exponential growth.