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

TL;DR

This paper investigates dynamic heterogeneities in glass-formers through theoretical and numerical methods, relating fluctuations to correlation functions and analyzing the effects of different dynamics and ensembles.

Contribution

It provides a theoretical framework linking fluctuations to dynamic susceptibilities and validates it with simulations across various glass-forming models.

Findings

Temperature dependence of correlations reveals dynamic lengthscales.

Choice of microscopic dynamics influences measured correlations.

Theoretical relations are confirmed by numerical simulations.

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.