Abstract
Low-dimensional, many-body systems are often characterized by ultraslow dynamics. We study a labelled particle in a generic system of identical particles with hard-core interactions in a strongly disordered environment. The disorder is manifested through intermittent motion with scale-free sticking times at the single particle level. While for a non-interacting particle we find anomalous diffusion of the power-law form of the mean squared displacement with , we demonstrate here that the combination of the disordered environment with the many-body interactions leads to an ultraslow, logarithmic dynamics with a universal exponent. Even when a characteristic sticking time exists but the fluctuations of sticking times diverge we observe the mean squared displacement with , that is slower than the famed Harris law without disorder. We rationalize the results in terms of a subordination to a counting process, in which each transition is dominated by the forward waiting time of an ageing continuous time process.
Highlights
Ultraslow, logarithmic time evolution of physical observables is remarkably often observed, for instance, for paper crumpling in a piston [1], DNA local structure relaxation [2], frictional strength [3], grain compactification [4], glassy systems [5], record statistics [6], as well as magnetization, conductance, and current relaxations in superconductors, spin glasses, and field-effect transistors [7]
From scaling arguments and simulations, we find that for the scale-free waiting time case 0 < α < 1, the tracer particle dynamics is ultra-slow with a logarithmic mean square displacement (MSD) x2(t)1/2
Stochastic dynamics governed by powerlaw forms of ψ(τ ), with 0 < α < 1 were shown to apply to tracer particle motion in the cytoplasm [11] in membranes [12] of living cells, in reconstituted actin networks [13], and determine the blinking dynamics of single quantum dots [14] as well as the dynamics involved in laser cooling [15]
Summary
Logarithmic time evolution of physical observables is remarkably often observed, for instance, for paper crumpling in a piston [1], DNA local structure relaxation [2], frictional strength [3], grain compactification [4], glassy systems [5], record statistics [6], as well as magnetization, conductance, and current relaxations in superconductors, spin glasses, and field-effect transistors [7]. From scaling arguments and simulations, we find that for the scale-free waiting time case 0 < α < 1, the tracer particle dynamics is ultra-slow with a logarithmic mean square displacement (MSD) x2(t) (log t)1/2.
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