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

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

2011-05-20

arxiv.org/abs/1105.4149v2

Phys. Rev. E 85, 021138 (2012)

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 14 figures; v2: extension from 2D to 3D and comparison with experiments

Scientific paper

10.1103/PhysRevE.85.021138

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 L\'evy glass) have found that the transmission probability T \propto 1/L^{\gamma} scales superdiffusively ({\gamma} < 1). The data has been interpreted in terms of a L\'evy walk. We present computer simulations to demonstrate that diffusive scaling ({\gamma} \approx 1) can coexist with a divergent second moment of the step size distribution (p(s) \propto 1/s^(1+{\alpha}) with {\alpha} < 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 L\'evy walk of independent steps.

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