Large time off-equilibrium dynamics of a manifold in a random potential

TL;DR

This paper investigates the long-time out-of-equilibrium behavior of an elastic manifold in a random potential, revealing universal scaling regimes and ultrametricity in slow aging dynamics through mean-field theory.

Contribution

It provides an analytical mean-field solution describing two distinct aging regimes and their universal scalings, including a crossover to ultrametricity in long-range correlated systems.

Findings

Identification of stationary and aging regimes in manifold dynamics

Universal scaling laws for two-time quantities

Crossover to ultrametricity in long-range correlations

Abstract

We study the out of equilibrium dynamics of an elastic manifold in a random potential using mean-field theory. We find two asymptotic time regimes: (i) stationary dynamics, (ii) slow aging dynamics with violation of equilibrium theorems. We obtain an analytical solution valid for all large times with universal scalings of two-time quantities with space. A non-analytic scaling function crosses over to ultrametricity when the correlations become long-range. We propose procedures to test numerically or experimentally the extent to which this scenario holds for a given system.