סמינר לפיזיקה של מערכות ביולוגיות וחומרים רכים: Universality in the onset of superdiffusion and anomalous transport in Lévy walks

Zoom: https://zoom.us/j/96051227115

Abstract: 

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 β_c=3/2. Above β_c, this correction scales as |x|~t^(1/2), describing simple diffusion. However, below β_c 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.