Spontaneous relaxation in generalized oscillator models with glassy dynamics

TL;DR

This paper introduces generalized oscillator models (GOMs) to analytically study aging and relaxation in glassy systems, providing exact solutions and insights into intermittency phenomena.

Contribution

The paper presents exactly solvable GOMs with new analytical expressions for effective temperature, advancing the theoretical understanding of aging and relaxation in glassy dynamics.

Findings

Analytic expressions for effective temperature in GOMs.

Validation of theoretical results through numerical simulations.

GOMs offer a framework for understanding intermittency in glasses.

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.