Aging and Glassy Dynamics in Complex Systems: Some Theoretical Ideas

Abstract

We discuss some recent experimental results on the non-stationary dynamics of spinglasses, which serves as an excellent laboratory for other complex systems. Inspired from Parisi's mean-field solution, we propose that the dynamics of these systems can be though of as a random walk in phase space, between traps characterized by trapping time distribution decaying as a power law. The average exploration time diverges in the spin-glass phase, naturally leading to time-dependent dynamics with a charateristic time scale fixed by the observation time t,. itself (aging). By the same token, we find that the correlation function (or the magnetization) decays as a stretched exponential at small times t < t. crossing over to power-law decay at large times t »> t,. Finally, we discuss recent speculations on the relevance of these concepts to real glasses, where quenched disorder is a priori absent.One of the most striking features of glassy dynamics is the aging phenomenon [1,2], that is, the fact that most physical properties strongly depend on the history of the sample, in particular the time t,,, elapsed since the quench from high temperature into the glass phase. For example, the a.c. susceptibility of a spin-glass at a frequency w decays towards its equilibrium value as (wt,)j-1, where x is an exponent less than 1. In fact, the full the response function R(t, t') does not depend on the difference t -t', as in usual equilibrium dynamics, but rather on the ratio 1. Since the equilibration time is infinite, the only relevant time scale can only be the experimental time itself. In this sense, time translation 347 Mat.