Equations of structural relaxation

TL;DR

This paper extends mode coupling theory equations to short times, enabling model-independent calculations of structural relaxation and providing new analytical tools, with an explicit demonstration of power-law relaxation at a glass transition.

Contribution

It introduces an extension of structural relaxation equations to short times, independent of microscopic dynamics assumptions, and demonstrates power-law relaxation at a glass transition in a schematic model.

Findings

Explicit proof of power-law relaxation at a glass transition.

Extension of equations to arbitrary short times.

New analytical starting points for studies of glass transition.

Abstract

In the mode coupling theory of the liquid to glass transition the long time structural relaxation follows from equations solely determined by equilibrium structural parameters. The present extension of these structural relaxation equations to arbitrarily short times on the one hand allows calculations unaffected by model assumptions about the microscopic dynamics and on the other hand supplies new starting points for analytical studies. As a first application, power-law like structural relaxation at a glass-transition singularity is explicitly proven for a special schematic MCT model.