Relationship between bond-breakage correlations and four-point correlations in heterogeneous glassy dynamics: Configuration changes and vibration modes

TL;DR

This paper explores the relationship between bond-breakage and four-point correlations in glassy systems, revealing how vibrational modes and configuration changes contribute to dynamic heterogeneities and their different timescales.

Contribution

It introduces a theoretical framework linking bond-breakage and four-point correlations, highlighting the role of vibration modes and system size effects in glassy dynamics.

Findings

Bond susceptibility chi_b(t) peaks when about half the bonds are broken.

Four-point susceptibility chi_4(t) captures combined heterogeneity and vibration effects.

Vibration modes significantly influence four-point correlations, especially in two dimensions.

Abstract

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor S_b(q,t) and the susceptibility chi_b(t) to detect the spatial correlations of configuration changes. Here chi_b(t) attains a maximum at t =t_b^max as a function of time t, where the fraction of the particles with broken bonds phi_b(t)$ is about 1/2. In the four-point scheme, treating the structure factor S_4(q,t) and the susceptibility chi_4(t), we detect superpositions of the heterogeneity of bond breakage and that of thermal low-frequency vibration modes. While the former grows slowly, the latter emerges quickly to exhibit complex space-time behavior. In two dimensions, the vibration modes extending over the system yield significant contributions to the four-point correlations, which depend on the system size logarithmically. A maximum of chi_4(t) is attained at t= t_4^max, where these two contributions become of the same order. As a result, t_4^max is considerably shorter than t_b^max.