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DY: Fachverband Dynamik und Statistische Physik

DY 57: Poster - Diffusion

DY 57.7: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

From integrated Brownian motion to Lévy walks — •Tony Albers and Günter Radons — Technische Universität Chemnitz, Germany

In a recent publication [1], we investigated the weakly nonergodic behavior of integrated Brownian motion. In this contribution, we will show how integrated Brownian motion can be mapped to a continuous time random walk with a spatiotemporal coupling of the form ψ(x,t)∝δ(|x|−t^3/2)t^−3/2, where ψ(x,t) describes the probability for the occurrence of a waiting time of duration t followed by a jump of length x. We investigate the nonergodic behavior of this Lévy walk by contrasting the time dependence of the ensemble-averaged and the time-averaged mean-squared displacement (MSD) and analyzing the random nature of the latter. Moreover, all quantities are studied in dependence on the ageing time which is the elapsed time between the beginning of the process and the beginning of the measurement. We compare our findings with the results obtained for integrated Brownian motion and discuss the similarities and differences.

[1] Tony Albers and Günter Radons, Phys. Rev. Lett. 113, 184101 (2014)