Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 71: Poster: Noneq. Stat. Phys., Stoch. Thermo, Brownian Dyn.

DY 71.15: Poster

Thursday, March 15, 2018, 15:30–18:00, Poster A

Statistical Distribution of the Area Inside Random Walks Which Return to Their Origin — •Vincent Sacksteder — Royal Holloway University of London

We study 2-D random walks, Levy flights, and Levy walks, using both analytical calculations and extensive Monte Carlo simulations. Counting only loops (walks which return to the origin), and examining the area A of these loops, we calculate the probability distribution of A. We find that the loop area distribution is proportional to the inverse of A for ordinary random walks and decreases more rapidly for Levy flights. The loop area distribution calculated here determines the quantum corrections to electrical conductivity in 2-D disordered systems, which are known as weak localization corrections.