Bouchaud's model exhibits two different aging regimes in dimension one

TL;DR

This paper investigates Bouchaud's model on a one-dimensional lattice, revealing two distinct aging regimes characterized by subaging behavior for certain parameter ranges.

Contribution

It demonstrates the existence of two different aging regimes in Bouchaud's model in one dimension, with rigorous proofs of subaging behavior under specific conditions.

Findings

Identification of two aging regimes in Bouchaud's model

Proof of subaging behavior for eta > 1 and a in [0,1]

Characterization of correlation functions over time

Abstract

Let E_i be a collection of i.i.d. exponential random variables. Bouchaud's model on Z is a Markov chain X(t) whose transition rates are given by w_{ij}=\nu \exp(-\beta ((1-a)E_i-aE_j)) if i, j are neighbors in Z. We study the behavior of two correlation functions: P[X(t_w+t)=X(t_w)] and P[X(t')=X(t_w) \forall t'\in[t_w,t_w+t]]. We prove the (sub)aging behavior of these functions when \beta >1 and a\in[0,1].