Geodesic
Wave transmission coefficients for one-dimensional random barriers
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 120-133 
A. V. Marchenko; S. A. Molchanov; L. A. Pastur. Wave transmission coefficients for one-dimensional random barriers. Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 120-133. http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a10/
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     author = {A. V. Marchenko and S. A. Molchanov and L. A. Pastur},
     title = {Wave transmission coefficients for one-dimensional random barriers},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {81},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1989_81_1_a10/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The logarithmic decrement $\gamma_D$ is studied for the wave transition coefficient in the case of a long one-dimensional random barrier described by the Markov type potential or by chaotically distributed $\delta$-function-like scatterers. The connection between $\gamma_D$ and $(-1)$ order moment of the amplitude of the Cauchy problem solution of the corresponding Schrödinger equation as well as the Lyapunov coefficient of this equation is established. Some asymptotics of $\gamma_D$ are also found.

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