# 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

Phys

- Rev. E 61 1164
- 2000

"J."

- PhilosophyThe New Yale Book of Quotations
- 2021

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