Aging dynamics in interacting many-body systems

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) $⟨x^2(t)⟩\simeq (\log t{)}^{1/2}$. This extreme slowing down compared to regular single file motion $⟨x^2(t)⟩\simeq t^{1/2}$ 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 $⟨x^2(t)⟩\simeq t^{\gamma }$, where $\gamma <1/2$, while for $\alpha >2$ we recover Harris law $\simeq t^{1/2}$.

5 pages, 4 figures

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