Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit

TL;DR

This paper analyzes the non-linear response of a one-dimensional disordered trap model under external forces, providing exact results in the strong disorder limit and exploring the transition from unbiased to directed regimes.

Contribution

It introduces a real-space renormalization approach that yields explicit, exact results for various observables in the strong disorder limit of the trap model.

Findings

Explicit scaling functions for diffusion front and other observables

Complete interpolation between unbiased and directed cases

Detailed analysis of regimes for average position based on times and external field

Abstract

We study the dynamics of the one dimensional disordered trap model presenting a broad distribution of trapping times $p(\tau) \sim 1/\tau^{1+\mu}$, when an external force is applied from the very beginning at $t=0$, or only after a waiting time $t_w$, in the linear as well as in the non-linear response regime. Using a real-space renormalization procedure that becomes exact in the limit of strong disorder $\mu \to 0$, we obtain explicit results for many observables, such as the diffusion front, the mean position, the thermal width, the localization parameters and the two-particle correlation function. In particular, the scaling functions for these observables give access to the complete interpolation between the unbiased case and the directed case. Finally, we discuss in details the various regimes that exist for the averaged position in terms of the two times and the external field.