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Universality in the onset of superdiffusion and anomalous transport in Lévy walks

TYPEStatistical & Bio Seminar
Speaker:Asaf Miron
Time:14:30 - 15:30
Location:Lidow Rosen Auditorium (323)

Anomalous dynamics in which local perturbations spread faster than diffusion are ubiquitously observed in the long-time behavior of a wide variety of systems.

The manner by which such systems evolve towards their asymptotic superdiffusive behavior is explored using the 1D Lévy walk of order 1<β<2.
The approach towards superdiffusion, as captured by the leading correction to the asymptotic propagator, is shown to undergo a transition as
β crosses the critical value 3/2. Above it, this correction scales as |x|~t^(1/2), describing simple diffusion. However, below the critical β it instead remains superdiffusive, scaling as |x|~t^(2β-1).

The transition is independent of the precise model details and is thus argued to be universal.

Such finite corrections typically play a crucial role in experimental and numerical studies of superdiffusive systems. This holds true both in equilibrium settings, as well as in nonequilibrium settings, where superdiffusion gives raise to anomalous transport.



×        AM, “Universality in the onset of superdiffusion in Lévy walks” - PRL 124, 140601 (2020)

×        AM, “Lévy walks on finite intervals: a step beyond asymptotics” - PRE 100, 012106 (2019)

×        AM, J. Cividini, A. Kundu, D. Mukamel,  "Derivation of fluctuating hydrodynamics and crossover from diffusive to anomalous transport in a hard-particle gas" PRE 99, 012124 (2019)