The Geometric Mean Squared Displacement and the Stokes-Einstein Scaling in a Supercooled Liquid

TL;DR

This paper proposes using the geometric mean of the van Hove distribution to better describe relaxation rates in supercooled liquids, improving the understanding of deviations from Stokes-Einstein scaling.

Contribution

It introduces the geometric mean squared displacement as a new approach to analyze relaxation, showing it reduces deviations from classical scaling laws.

Findings

Geometric mean better captures relaxation in supercooled liquids.

Increased non-Gaussianity amplifies differences between means.

Geometric diffusion constant reduces deviation from Stokes-Einstein scaling.

Abstract

It is proposed that the rate of relaxation in a liquid is better described by the geometric mean of the van Hove distribution function, rather than the standard arithmetic mean used to obtain the mean squared displacement. The difference between the two means is shown to increase significantly with an increase in the non-Gaussian character of the displacement distribution. Preliminary results indicate that the geometric diffusion constant results in a substantial reduction of the deviation from Stokes-Einstein scaling.