Nonalgebraic length dependence of transmission through a chain of barriers with a Lévy spacing distribution

@article{Beenakker2009NonalgebraicLD,
  title={Nonalgebraic length dependence of transmission through a chain of barriers with a L{\'e}vy spacing distribution},
  author={C. W. J. Beenakker and Christoph Groth and A. Akhmerov},
  journal={Physical Review B},
  year={2009},
  volume={79},
  pages={024204}
}
The recent realization of a ``L\'evy glass'' (a three-dimensional optical material with a L\'evy distribution of scattering lengths) has motivated us to analyze its one-dimensional analog: A linear chain of barriers with independent spacings $s$ that are L\'evy distributed: $p(s)\ensuremath{\propto}{s}^{\ensuremath{-}1\ensuremath{-}\ensuremath{\alpha}}$ for $s\ensuremath{\rightarrow}\ensuremath{\infty}$. The average spacing diverges for $0l\ensuremath{\alpha}l1$. A random walk along such a… 

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References

SHOWING 1-10 OF 18 REFERENCES
Editors
  • Computer Science
    Brain Research Bulletin
  • 1986
Phys
  • Rev. E 61 1164
  • 2000
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)
Phys
  • Rev. B 34, 445
  • 1986
Phys
  • Rep. 339, 1
  • 2000
The Fractal Geometry of Nature (Freeman
  • New York,
  • 1983
Solid State Comm
  • 132, 59
  • 2004
Phys
  • Rev. E 58, 4254
  • 1998
Phys
  • Rev. B 64, 134209
  • 2001
Phys
  • Lett. A 169, 103
  • 1992
...
...