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

@article{Groth2012TransmissionPT,
  title={Transmission probability through a L{\'e}vy glass and comparison with a L{\'e}vy walk.},
  author={Christoph Groth and A. Akhmerov and C. W. J. Beenakker},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2012},
  volume={85 2 Pt 1},
  pages={
          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 so-called Lévy glass) have found that the transmission probability T∝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≈1) can coexist with a divergent second moment of the step size distribution [p(s)∝1/s(1+α) with α<2]. This finding is in… 
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References

SHOWING 1-10 OF 14 REFERENCES
Editors
  • Computer Science
    Brain Research Bulletin
  • 1986
Nature 453
  • 495
  • 2008
Phys
  • Rev. E 84, 021105
  • 2011
Phys
  • Rev. E 61, 1164
  • 2000
Phys
  • Rev. Lett. 74, 4959
  • 1995
Kazakov
  • M. G. E. da Luz, E. P. Raposo, H. E. Stanley, and G. M. Viswanathan, Phys. Rev. E 64, 041108 (2001); S. V. Buldyrev et al., Physica A 302, 148
  • 2001
Phys
  • Rev. E 82, 011101
  • 2010
Phys
  • Rev. E 58, 4254
  • 1998
Phys
  • Rev. E 81, 060101(R) (2010); R. Burioni, L. Caniparoli, S. Lepri, and A. Vezzani, Phys. Rev. E 81, 011127 (2010); A. Vezzani, R. Burioni, L. Caniparoli, and S. Lepri, Phil. Mag. 91, 1987
  • 2011
Phys
  • Rev. B 79, 024204
  • 2009
...
...