Non-Gaussianity of van Hove Function and Dynamic Heterogeneity Length Scale

TL;DR

This paper investigates how the non-Gaussian behavior of particle displacements in supercooled liquids relates to the dynamic heterogeneity length scale, revealing a crossover from non-Gaussian to Gaussian distributions at this scale.

Contribution

It demonstrates that non-Gaussianity in the van Hove function occurs at the dynamic heterogeneity length scale and provides a method to measure this scale through systematic coarse graining.

Findings

The non-Gaussianity of the van Hove function diminishes at the heterogeneity length scale.

The measured heterogeneity scale agrees with values from other methods.

Dynamic behavior becomes homogeneous when coarse grained over this length scale.

Abstract

Non-Gaussian nature of the probability distribution of particles' displacements in the supercooled temperature regime in glass-forming liquids are believed to be one of the major hallmarks of glass transition. It is already been established that this probability distribution which is also known as the van Hove function show universal exponential tail. The origin of such an exponential tail in the distribution function is attributed to the hopping motion of particles observed in the supercooled regime. The non-Gaussian nature can also be explained if one assumes that the system has heterogeneous dynamics in space and time. Thus exponential tail is the manifestation of dynamic heterogeneity. In this work we directly show that non-Gaussanity of the distribution of particles' displacements occur over the dynamic heterogeneity length scale and dynamical behaviour course grained over this length scale becomes homogeneous. We study the non-Gaussianity of van Hove function by systematically coarse graining at different length scale and extract the length scale of dynamic heterogeneity at which the shape of the van Hove function crosses over from non-Gaussian to Gaussian. The obtained dynamic heterogeneity scale is found to be in very good agreement with the scale obtained from other conventional methods.