Efficient numerical method for studying random walks on disordered structuresT. B. Schrøder
DNRF centre "Glass and Time", IMFUFA, Department of Sciences, Roskilde University Postbox 260, DK-4000 Roskilde, Denmark and Nordita - Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
received 20 June 2007; accepted in final form 24 November 2007; published February 2008
published online 19 December 2007
A method for efficient numerical calculation of the frequency-dependent diffusion coefficient of random walks on disordered structures is presented. The method relies on solving the linear system of equations for probability currents in the frequency domain; consequently, the noise associated with traditional Monte Carlo simulation is avoided, and systems with extremely long relaxation times can be studied. Results are reported for two models on the square lattice: i) the random site-energy model and ii) a random walk at the percolation threshold for site percolation.
02.70.-c - Computational techniques; simulations.
05.40.Fb - Random walks and Levy flights.
66.30.Dn - Theory of diffusion and ionic conduction in solids.
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