Abstract:
The logarithmic damping rate of the coeffficient of transmission, averaged over the scatterer configurations, of a long one-dimensional barrier is expanded in powers of the scatterer concentration, and this expansion is analyzed. It is shown that the damping rate is analytic at low concentrations and for nonresonant scattering in both the case of completely
randomly distributed scatterers as well as when there are statistical correlations in their distribution. The technique of the proof is analogous to the technique employed with the Kirkwood–Salsburg correlation equations of statistical physics.
Citation:
A. V. Marchenko, L. A. Pastur, “Transmission of waves and particles through long random barriers”, TMF, 68:3 (1986), 433–448; Theoret. and Math. Phys., 68:3 (1986), 929–940
\Bibitem{MarPas86}
\by A.~V.~Marchenko, L.~A.~Pastur
\paper Transmission of waves and particles through long random barriers
\jour TMF
\yr 1986
\vol 68
\issue 3
\pages 433--448
\mathnet{http://mi.mathnet.ru/tmf5196}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=871064}
\transl
\jour Theoret. and Math. Phys.
\yr 1986
\vol 68
\issue 3
\pages 929--940
\crossref{https://doi.org/10.1007/BF01019395}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1986G881200011}
Linking options:
https://www.mathnet.ru/eng/tmf5196
https://www.mathnet.ru/eng/tmf/v68/i3/p433
This publication is cited in the following 5 articles:
Vadim Kostrykin, Robert Schrader, “A random necklace model”, Waves in Random Media, 14:1 (2004), S75
V. Kostrykin, R. Schrader, “The generalized star product and the factorization of scattering matrices on graphs”, Journal of Mathematical Physics, 42:4 (2001), 1563
V. KOSTRYKIN, R. SCHRADER, “SCATTERING THEORY APPROACH TO RANDOM SCHRÖDINGER OPERATORS IN ONE DIMENSION”, Rev. Math. Phys., 11:02 (1999), 187
A. V. Marchenko, S. A. Molchanov, L. A. Pastur, “Wave transmission coefficients for one-dimensional random barriers”, Theoret. and Math. Phys., 81:1 (1989), 1096–1106
L. A. Pastur, “A limit theorem for sums of exponentials”, Math. Notes, 46:3 (1989), 712–716
Citation in format AMSBIB
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