Transmission probability through a Lévy glass and comparison with a Lévy walk
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 so-called Lévy glass) have found that the transmission probability T∝1/Lγ 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≈1) can coexist with a divergent second moment of the step size distribution [p(s)∝1/s1+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.
- Publication:
-
Physical Review E
- Pub Date:
- February 2012
- DOI:
- 10.1103/PhysRevE.85.021138
- arXiv:
- arXiv:1105.4149
- Bibcode:
- 2012PhRvE..85b1138G
- Keywords:
-
- 05.40.Fb;
- 05.60.Cd;
- 42.25.Bs;
- 42.25.Dd;
- Random walks and Levy flights;
- Classical transport;
- Wave propagation transmission and absorption;
- Wave propagation in random media;
- Condensed Matter - Disordered Systems and Neural Networks
- E-Print:
- 10 pages, 14 figures