Linear and non linear response in the aging regime of the 1D trap model

TL;DR

This paper explores the response behavior of the 1D trap model during aging, revealing multiple scaling regimes and confirming the fluctuation dissipation relation's validity even out of equilibrium.

Contribution

It introduces a detailed analysis of the response function in the 1D trap model, identifying various scaling regimes and validating the fluctuation dissipation relation during aging.

Findings

Multiple scaling regimes depending on t, tw, and h

Fluctuation dissipation relation holds during aging

Numerical simulations confirm scaling arguments

Abstract

We investigate the behaviour of the response function in the one dimensional trap model using scaling arguments that we confirm by numerical simulations. We study the average position of the random walk at time tw+t given that a small bias h is applied at time tw. Several scaling regimes are found, depending on the relative values of t, tw and h. Comparison with the diffusive motion in the absence of bias allows us to show that the fluctuation dissipation relation is, in this case, valid even in the aging regime.