Dresden 2017 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 60: Posters - Brownian Motion, Noise

DY 60.3: Poster

Thursday, March 23, 2017, 17:00–19:30, P1A

Weak nonergodicity in a generalized Lévy walk model — •Tony Albers and Günter Radons — Technische Universität Chemnitz, Germany

In this contribution, we investigate the weakly nonergodic behavior of a generalized Lévy walk in which the velocities of the flights depend on the durations of the flights in a nonlinear way. This process essentially depends on two characteristic exponents determining the distribution of flight durations and the deterministic dependence of the flight velocities on the durations of the flights. We compare for this model of anomalous diffusion the temporal behavior of the ensemble-averaged squared displacement with the time-averaged squared displacement and quantify the randomness of the latter with a scatter distribution and the ergodicity breaking parameter. We find regions in the two-dimensional parameter space which show manifestations of weak nonergodicity which have never been observed before in the literature. Moreover, we provide a simple explanation for the observed transitions between different kinds of anomalous diffusion and weak nonergodicity by a divergence of six different characteristic quantities of the random walk.