Aging dynamics in interacting many-body systems

TL;DR

This paper investigates aging and ultra-slow dynamics of a tracer particle in a disordered, interacting many-body system, revealing logarithmic and subdiffusive behaviors depending on the waiting time distribution.

Contribution

It introduces a model of interacting particles with power-law waiting times, showing novel ultra-slow logarithmic diffusion for 0<α<1 and subdiffusive regimes for other α values.

Findings

Logarithmic mean square displacement for 0<α<1

Subdiffusive MSD with exponent γ<1/2 for 1<α<2

Recovery of normal single-file diffusion for α>2

Abstract

Low-dimensional, complex systems are often characterized by logarithmically slow dynamics. We study the generic motion of a labeled particle in an ensemble of identical diffusing particles with hardcore interactions in a strongly disordered, one-dimensional environment. Each particle in this single file is trapped for a random waiting time $\tau$ with power law distribution $\psi(\tau)\simeq\tau^{-1- \alpha}$, such that the $\tau$ values are independent, local quantities for all particles. From scaling arguments and simulations, we find that for the scale-free waiting time case $0<\alpha<1$, the tracer particle dynamics is ultra-slow with a logarithmic mean square displacement (MSD) $\langle x^2(t)\rangle\simeq(\log t)^{1/2}$. This extreme slowing down compared to regular single file motion $\langle x^2(t)\rangle\simeq t^{1/2}$ is due to the high likelihood that the labeled particle keeps encountering strongly immobilized neighbors. For the case $1<\alpha<2$ we observe the MSD scaling $\langle x^2(t)\rangle\simeq t^{\gamma}$, where $\gamma<1/2$, while for $\alpha>2$ we recover Harris law $\simeq t^{1/2}$.