Spontaneous relaxation in generalized oscillator models with glassy dynamics

Abstract

In this paper we introduce the generalized oscillator model (GOM) as a family of exactly solvable models useful to investigate theoretical aspects related to the statistical description of the aging state. GOMs are defined by a potential function V(x) and characterized by a zero-temperature relaxation determined by entropy barriers and partial equilibration. Analytic expressions for the effective temperature can be derived using a fluctuation theorem valid in the aging regime without the need to solve the dynamical equations for correlations and responses. Two classes of models are investigated in detail: the homogeneous potential model with V(x)=(k/2p)x^{2p} (p being a positive integer) and the wedge potential model (V(x)=k|x|) where V(x) has a singularity at the ground state coordinate x=0. For the latter, we present some numerical simulations that reinforce the validity of the main analytical results. GOMs offer a conceptual framework to develop a statistical description of the spontaneous relaxation process that has been recently proposed to be at the root of the intermittency phenomenon observed in glasses and colloids.

Latex file, 21 pages, Contribution to the special issue 'Hans C. Andersen Festschrift'