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We investigate the dynamic heterogeneities of glassy particle systems in thetheoretical schemes of bond breakage and four-point correlation functions. Inthe bond-breakage scheme, we introduce the structure factor S_b(q,t) and thesusceptibility chi_b(t) to detect the spatial correlations of configurationchanges. 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 thesusceptibility chi_4(t), we detect superpositions of the heterogeneity of bondbreakage and that of thermal low-frequency vibration modes. While the formergrows slowly, the latter emerges quickly to exhibit complex space-timebehavior. In two dimensions, the vibration modes extending over the systemyield significant contributions to the four-point correlations, which depend onthe 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.

physical review. e, statistical, nonlinear and soft matter physics

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