Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics

Abstract

We study theoretically and numerically a family of multi-point dynamic susceptibilities that quantify the strength and characteristic lengthscales of dynamic heterogeneities in glass-forming materials. We use general theoretical arguments (fluctuation-dissipation relations and symmetries of relevant dynamical field theories) to relate the sensitivity of averaged two-time correlators to temperature and density to spontaneous fluctuations of the local dynamics. Our theoretical results are then compared to molecular dynamics simulations of the Newtonian, Brownian and Monte-Carlo dynamics of two representative glass-forming liquids, a fragile binary Lennard-Jones mixture and a model for the strong glass-former silica. We justify in detail the claim made in [Science 310, 1797 (2005)], that the temperature dependence of correlation functions allows one to extract useful information on dynamic lengthscales in glassy systems. We also discuss some subtle issues associated to the choice of microscopic dynamics and of statistical ensemble through conserved quantities, which are found to play an important role in determining dynamic correlations.

24 pages, 7 figs - Several discussions added (Arrhenius systems, hydrodynamic contributions, relation between susceptibilities and lengthscales, etc.)

References in corpus (8)

• Glassy dynamics of kinetically constrained models
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Lengthscale dependence of dynamic four-point susceptibilities in glass formers
• Structural and dynamical heterogeneity in a glass forming liquid
• Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices
• Four-point susceptibility of a glass-forming binary mixture: Brownian dynamics

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