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Iterated Function System and Diffusion in the Presence of Disorder and Traps

Thomas Wichmann·Achille Giacometti·K. P. N. Murthy
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Abstract

The escape probability $ξ_{x}$ from a site $x$ of a one-dimensional disordered lattice with trapping is treated as a discrete dynamical evolution by random iterations over nonlinear maps parametrized by the right and left jump probabilities. The invariant measure of the dynamics is found to be a multifractal. However the measure becomes uniform over the support when the disorder becomes weak for any non-zero trapping probability. Implications of our findings in terms of diffusion are discussed.

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Thomas Wichmann, Achille Giacometti, K. P. N. Murthy. 1995-03-15. Iterated Function System and Diffusion in the Presence of Disorder and Traps. https://doi.org/10.1103/physreve.52.481

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