Correlation and response in the Backgammon model: the Ehrenfest legacy

TL;DR

This paper analytically investigates the aging, response, and fluctuation-dissipation ratios in the low-temperature dynamics of the Backgammon model, revealing detailed scaling behaviors and crossover phenomena.

Contribution

It provides a comprehensive analytical study of correlation and response functions in the Backgammon model, including aging and crossover behaviors at low temperatures.

Findings

Scaling behavior of local correlation functions

Analysis of fluctuation-dissipation ratios

Characterization of aging and equilibrium crossover

Abstract

We pursue our investigation of the non-equilibrium dynamics of the Backgammon model, a dynamical urn model which exhibits aging and glassy behavior at low temperature. We present an analytical study of the scaling behavior of the local correlation and response functions of the density fluctuations of the model, and of the associated fluctuation- dissipation ratios, throughout the alpha regime of low temperatures and long times. This analysis includes the aging regime, the convergence to equilibrium, sand the crossover behavior between them.