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

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 Sb(q,t) and the susceptibility χb(t) to detect the spatial correlations of configuration changes. Here χb(t) attains a maximum at t=tbmax as a function of time t, where the fraction of the particles with broken bonds φb(t) is about 1/2. In the four-point scheme, treating the structure factor S4(q,t) and the susceptibility χ4(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 χ4(t) is attained at t=t4max, where these two contributions become of the same order. As a result, t4max is considerably shorter than tbmax.