Nonequilibrium dynamics of a simple stochastic model

TL;DR

This paper analyzes the low-temperature nonequilibrium dynamics of a simple stochastic model relevant to glasses, focusing on aging, relaxation, and fluctuation-dissipation behavior.

Contribution

It provides an analytical study of the scaling behavior of energy, correlations, and response functions during aging and convergence to equilibrium in a simple glassy model.

Findings

Characteristic time diverges exponentially at low temperature.

Aging regime exhibits specific scaling behavior.

Crossover from aging to equilibrium is characterized analytically.

Abstract

We investigate the low-temperature dynamics of a simple stochastic model, introduced recently in the context of the physics of glasses. The slowest characteristic time at equilibrium diverges exponentially at low temperature. On smaller time scales, the nonequilibrium dynamics of the system exhibits an aging regime. We present an analytical study of the scaling behaviour of the mean energy, of its local correlation and response functions, and of the associated fluctuation-dissipation ratio throughout the regime of low temperature and long times. This analysis includes the aging regime, the convergence to equilibrium, and the crossover behaviour between them.