Aging dynamics in interacting many-body systems

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) $⟨x^2(t)⟩\simeq (\log t{)}^{1\mathrm{/}2}$. 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$\gamma<1/2$,whilefor$\alpha>2$werecoverHarrislaw$\simeq t^{1/2}$.