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arXiv · 1105.4149

Transmission probability through a Lévy glass and comparison with a Lévy walk

C. W. Groth·A. R. Akhmerov·C. W. J. Beenakker
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Abstract

Recent experiments on the propagation of light over a distance L through a random packing of spheres with a power law distribution of radii (a socalled Lévy glass) have found that the transmission probability T \propto 1/L^γ scales superdiffusively (γ < 1). The data has been interpreted in terms of a Lévy walk. We present computer simulations to demonstrate that diffusive scaling (γ \approx 1) can coexist with a divergent second moment of the step size distribution (p(s) \propto 1/s^(1+α) with α < 2). This finding is in accord with analytical predictions for the effect of step size correlations, but deviates from what one would expect for a Lévy walk of independent steps.

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C. W. Groth, A. R. Akhmerov, C. W. J. Beenakker. 2012-01-14. Transmission probability through a Lévy glass and comparison with a Lévy walk. https://doi.org/10.1103/physreve.85.021138

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