Out-of-equilibrium dynamical fluctuations in glassy systems

Abstract

In this paper we extend the earlier treatment of out-of-equilibrium mesoscopic fluctuations in glassy systems in several significant ways. First, via extensive simulations, we demonstrate that models of glassy behavior without quenched disorder display scalings of the probability of local two-time correlators that are qualitatively similar to that of models with short-ranged quenched interactions. The key ingredient for such scaling properties is shown to be the development of a criticallike dynamical correlation length, and not other microscopic details. This robust data collapse may be described in terms of a time-evolving ''extreme value'' distribution. We develop a theory to describe both the form and evolution of these distributions based on a effective model approach.

Beyond simple exponential correlation functions and equilibrium dynamics in x-ray photon correlation spectroscopy

“…Examples of such dynamics have been nicely demonstrated in a series of recent DLS experiments on soft glassy materials by Cipelletti and co-workers [31,51,57,58]. In other examples, theoretical models of glassy systems both with and without quenched disorder have revealed temporal auto-correlations with an asymmetric distribution that resembles the Gumbel form prevalent in extreme value statistics [59]- [62]; by analyzing the fluctuations in the degree of correlation, such behavior could possibly be experimentally demonstrated.…”

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

“…It is further the asymptotic distributions of the extreme values of sequences correlated over a 'distance' 1/a (eq.15) [46] and the asymptotic distribution of sums of independent non identically distributed random variables or of correlated variables which do not verify the conditions of validity of the central limit theorem [47]. The generalized Gumbel distribution reads:…”

Fluctuations in the time variable and dynamical heterogeneity in glass-forming systems

“…This framework is based on the hypothesis that in glassy systems the long time dynamics is invariant under reparametrizations of the time variable [20][21][22][23][24][25][26][27][28], but this invariance is broken, giving rise to Goldstone modes that manifest themselves with the emerge of heterogeneous dynamics [20][21][22][23][24][29][30][31][32][33][34]. The Goldstone modes correspond to fluctuations in the time reparametrization t → φ r (t), i.e.…”