Quasi-equilibrium in glassy dynamics: a liquid theory approach

Abstract

We introduce a quasi-equilibrium formalism in the theory of liquids in order to obtain a set of coarse grained long time dynamical equations for the two point density correlation functions. Our scheme allows to use typical approximations devised for equilibrium to study long time glassy dynamics. We study the Hypernetted Chain (HNC) approximation and a recent closure scheme by Szamel. In both cases we get dynamical equations that have the structure of the Mode-Coupling (MCT) equations in the long time region. The HNC approach, that was so far used to get equilibrium quantities is thus generalized to a fully consistent scheme where long-time dynamic quantities can also be computed. In the context of this approximation we get an asymptotic description of both equilibrium glassy dynamics at high temperature and of aging dynamics at low temperature. The Szamel approximation on the other hand is shown to lead to the exact Mode Coupling equation of Götze for equilibrium dynamics. We clarify the way phase space is sampled according to MCT during dynamical relaxation.

Version accepted for publication in Journal of Physics A: Mathematical and Theoretical, Fast Track Communications

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• Quasi equilibrium construction for the long time limit of glassy dynamics
• Clever algorithms for glasses work by time reparametrization
• Free-energy functional of instantaneous correlation field in liquids: field-theoretic derivation of the closures
• Following the evolution of metastable glassy states under external perturbations: compression and shear-strain
• An alternative, dynamic density functional-like theory for time-dependent density fluctuations in glass-forming fluids