Super-Cooled Liquids: Equivalence between Mode-Coupling Theory and Replica Approach

TL;DR

This paper demonstrates that the replica approach and Mode-Coupling Theory offer equivalent descriptions of the critical dynamics in the beta-regime of super-cooled liquids, bridging static and dynamic perspectives.

Contribution

It establishes a quantitative and qualitative equivalence between the replica approach and Mode-Coupling Theory for super-cooled liquids' critical dynamics.

Findings

Replica approach characterizes critical dynamics similarly to Mode-Coupling Theory.

The equivalence holds both qualitatively and quantitatively.

Discussion connects this equivalence to open problems in current theory.

Abstract

We show that the replica approach to glassy dynamics provides, in spite of its static nature, a characterization of critical dynamics in the $\beta$-regime of super-cooled liquids that is equivalent to the one of Mode-Coupling-Theory, both qualitatively and quantitatively. The nature and extent of this equivalence is discussed in connection to the main open problems of the current theory.