Dresden 2014 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 4: Anomalous Diffusion

DY 4.1: Talk

Monday, March 31, 2014, 09:30–09:45, ZEU 146

Lévy walks, random time averaged diffusivities and a no-go theorem for ergodicity and an Einstein Relation — •Daniela Froemberg — Max Planck Institute for the Physics of Complex Systems, Dresden

We investigate a Lévy walk alternating between two states characterized by velocities of opposite sign. The sojourn times in either state are drawn according to power law probability distribution functions (pdf). Two different regimes are considered: The first case where the sojourn time pdf lacks its mean, corresponds to a ballistic regime. In the second case the mean of the sojourn time pdf exists while the second moment does not, which results in enhanced diffusion. The correlation functions and the discrepancies between time averaged and ensemble averaged mean squared displacements are investigated. The ballistic case exhibits weak ergodicity breaking and the fluctuations of the shifted time averaged mean squared displacements are universal. In the enhanced diffusion regime, the fluctuations of the time averaged mean squared displacements vanish at large times, yet very slowly. Moreover, we consider an external bias and present a no-go theorem for the generalized Einstein relation and ergodicity in the sense of equal time and ensemble averages.