2001/04/17 by Bernd Rinn, Philipp Maass, Jean‐Philippe Bouchaud +1
Economics, Econometrics and Finance · Materials Science · Physics and Astronomy · #Complex Systems and Time Series Analysis #Material Dynamics and Properties #Theoretical and Computational Physics #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1103/physrevb.64.104417
16 pages, 10 figures
arxiv created 2001/04/17 · openalex publication_date 2001/08/22 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Aging dynamics in glassy systems is investigated by considering the hopping motion in a rugged energy landscape whose deep minima are characterized by an exponential density of states \ensuremathρ(E)=Tg^\ensuremath-1exp(E/Tg), \ensuremath-\ensuremath∞<E<~0. In particular we explore the behavior of a generic two-time correlation function \ensuremathΠ(tw+t,tw) below the glass transition temperature Tg when both the observation time t and the waiting time tw become large. We show the occurrence of ordinary scaling behavior, \ensuremathΠ(tw+t,tw)\ensuremath∼F1(t/tw^\ensuremathμ1), where \ensuremathμ1=1 (normal aging) or \ensuremathμ1<1 (subaging), and the possible simultaneous occurrence of generalized scaling behavior, tw^\ensuremathγ[1\ensuremath-\ensuremathΠ(tw+t,tw)]\ensuremath∼F2(t/tw^\ensuremathμ2) with \ensuremathμ2<\ensuremathμ1 (subaging). Which situation occurs depends on the form of the effective transition rates between the low-lying states. Employing a ``partial equilibrium concept,'' the exponents \ensuremathμ1,2 and the asymptotic form of the scaling functions are obtained both by simple scaling arguments and by analytical calculations. The predicted scaling properties compare well with Monte Carlo simulations in dimensions d=1\ensuremath-1000 and it is argued that a mean-field-type treatment of the hopping motion fails to describe the aging dynamics in any dimension. Implications for more general situations involving different forms of transition rates and the occurrence of many scaling regimes in the t\ensuremath-tw plane are pointed out.