Mesoscopic fluctuations and intermittency in aging dy - namics

– The configurational de-correlation in an aging system is attributed to irreversible intermittent rearrangements, which are described as a Poisson process with average ∝ ln(1 + t/tw), where t is the observation time and tw is the age [P. Sibani and H.J. Jensen, Europhys. Lett. 69, 2005]. On this basis, we obtain a simple model for the off-equilibrium aging behavior of the autocorrelation: the average autocorrelation decays algebraically, and its shifted and rescaled probability density function (PDF) has a Gumbel-like shape which approaches a Gaussian at large times and becomes sharp in the thermodynamic limit. The model properties are tested against simulations of the Edwards-Anderson spin glass, and are in reasonable agreement with other available data. Introduction. – After a rapid change of an external parameter, e.g. a temperature quench, the properties of aging materials slowly evolve with the age tw, i.e. the time elapsed from the initial change. Since the phenomenon was first observed in polymers [1], evidence has accumulated that many complex materials, among others spin-glasses [2], type II superconductors [3], glasses [4], and soft condensed matter [5], have similar aging properties, e.g. : For observation times t ≪ tw averages are nearly constant, and autocorrelations and their conjugate linear response functions are connected by an equilibrium-like fluctuation-dissipation theorem (FDT). For t ≫ tw the FDT is violated and physical averages visibly drift. As recently discovered, this happens in an intermittent fashion [6, 7], i.e. through rare, large, and spatially heterogeneous re-arrangements. These manifests themselves as non-Gaussian tails in the probability density function (PDF) of configurational probes such as colloidal particle displacement [8,9] and correlation [10] or voltage noise fluctuations in glasses [11]. In this Letter, intermittent events, for short quakes, are considered the main source of de-correlation in the non-equilibrium aging regime. Using the idea [12, 13] that quakes are irreversible and triggered by energy fluctuations of record magnitude, we formulate a simplified model for the aging behavior of the autocorrelation PDF. The predictions, which are partly analytical, agree with macroscopic and mesoscopic data from the literature and with the spin-glass simulations presented here. They include a power-law decay of the average correlation [14], and a left-skewed autocorrelation PDF. The latter resembles colloidal gels data [10] and data for spin-glasses and kinetically constrained models [15, 16], and is closely approximated by Gumbel distributions [16, 17].