Transmission probability through a L\'evy glass and comparison with a L\'evy walk
| Autor: | Groth, C. W., Akhmerov, A. R., Beenakker, C. W. J. |
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| Rok vydání: | 2011 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 85, 021138 (2012) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.85.021138 |
| Popis: | 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. Comment: 10 pages, 14 figures; v2: extension from 2D to 3D and comparison with experiments |
| Databáze: | arXiv |
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