Geodesic
Wave transmission coefficients for one-dimensional random barriers
Teoretičeskaâ i matematičeskaâ fizika, Tome 81 (1989) no. 1, pp. 120-133 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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     title = {Wave transmission coefficients for one-dimensional random barriers},
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}
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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/

[1] Lifshits I. M., Kirpichenkov V. Ya., ZhETF, 77:3 (1979), 989–1016 | MR

[2] Lifshits I. M., Gredeskul S. A., Pastur L. A., Vvedenie v teoriyu neuporyadochennykh sistem, Nauka, M., 1982 | MR

[3] Lifshits I. M., Gredeskul S. A., Pastur L. A., ZhETF, 83:6 (1982), 2362–2376

[4] Marchenko A. V., Pastur L. A., TMF, 68:3 (1986), 433–448 | MR

[5] Molchanov S. A., Izv. AN SSSR, ser. matem., 42:1 (1978), 70–103 | MR | Zbl

[6] Goldsheid I. Ya., Molchanov S. A., Pastur L. A., Funkts. analiz i ego prilozh., 11:1 (1977), 1–10 | MR

[7] Pastur L. A., Feldman E. P., ZhETF, 67:2 (1974), 487–493

[8] Gikhman I. I., Skorokhod A. V., Vvedenie v teoriyu sluchainykh protsessov, Nauka, M., 1977 | MR

[9] Gertner Yu., Teor. veroyatn. i ee primen., 21:1 (1976), 95–106 | MR

[10] Venttsel A. D., Freidlin M. I., Fluktuatsii v dinamicheskikh sistemakh pod deistviem malykh sluchainykh vozmuschenii, Nauka, M., 1979 | MR | Zbl

[11] Minlos R. A., Povzner A. Ya., Tr. MMO, 17, 1967, 243–272

[12] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR | Zbl

[13] Arnold L., Papanicolaou G., Wihstnutz V., CIAM J. Appl. Math., 46:3 (1986), 427–450 | MR | Zbl

[14] Perel V. I., Polyakov D. G., ZhETF, 86:1 (1984), 352–366

[15] Benderskii M. M., Pastur L. A., ZhETF, 57:1 (1969), 284–294 | MR