Ergodicity in glass relaxation

TL;DR

This paper derives a new equation for glass relaxation that indicates ergodicity, showing the density correlation decays to zero and introducing force fluctuation as a potential indicator of structural transitions.

Contribution

It presents a novel derivation of the glass relaxation equation without using the Zwanzig-Mori method, revealing ergodic behavior and proposing force fluctuation as a structural transition marker.

Findings

Density correlation function decays to zero, indicating ergodicity.

Force fluctuation of individual particles is temperature-sensitive.

Simplified static solution obtained for long-time behavior.

Abstract

We derive an equation for the glass relaxation. In the derivation, the Zwanzig-Mori projection method is not applied explicitly, which makes our equation different from the mode coupling theory. Due to the nonlinearity, it is difficult to solve the equation to get the full behaviors of the glass relaxation. But we can simplify the equation when time approaches infinity and obtain the static result analytically. The static result shows that the density correlation function decays to zero finally, meaning that the glass relaxation is ergodic. In this study, we also find that the force fluctuation of one individual particle averaged in the glass is sensitive to the temperature and is suggested to be a parameter to reflect the structural transition for the glass relaxation.