×
Doron, E.; Smilansky, U.; Frenkel, A.

Chaotic scattering and transmission fluctuations. (English) Zbl 0741.58053

Physica D 50, No. 3, 367-390 (1991).
The authors studied the consequences of the classical chaotic dynamics on the propagation of waves in simple devices. Using S matrix method they prove that the transmission and reflection coefficient fluctuate when the wavelength is varied. The statistics of the fluctuations follow the predictions of the theory of random matrices.
Reviewer: I.Grosu (Iaşi)

Cited in 3 Documents

MSC:

58Z05 Applications of global analysis to the sciences
15B52 Random matrices (algebraic aspects)

Keywords:

chaotic dynamics; propagation of waves; matrix method; transmission; reflection; fluctuations; random matrices
Cite Review PDF
Full Text: DOI

References:

[1] Washburn, S.; Webb, R. A., Adv. Phys., 35, 375 (1986)
[2] Beenakker, C. W.J.; van Houten, H., Phys. Rev. Lett., 60, 2406 (1988)
[3] Baranger, H. U.; Stone, A. D., Phys. Rev. Lett., 63, 414 (1989)
[4] Timp, G.; Chang, A. M.; Mankiewich, P.; Behringer, R.; Cunningham, J. E.; Chang, T. Y.; Howard, R. E., Phys. Rev. Lett., 59, 732 (1987)
[5] Timp, G.; Baranger, H. U.; de Vegar, P.; Cunningham, J. E.; Howard, R. E.; Behringer, R.; Mankiewich, P. M., Phys. Rev. Lett., 60, 2081 (1988)
[6] Ford, C. J.B.; Washburn, S.; Büttiker, M.; Knoedler, C. M.; Hong, J. M., Phys. Rev. Lett., 62, 2724 (1989)
[7] Chang, A. M.; Chang, T. Y.; Baranger, H. U., Phys. Rev. Lett., 63, 996 (1989)
[8] Imry, Y., Europhysics Lett., 1, 249 (1986)
[9] Cvitanović, P.; Eckhardt, B., Phys. Rev. Lett., 63, 823 (1989)
[10] Gaspard, P.; Rice, S. A., J. Chem. Phys., 90, 2225 (1989)
[11] Gaspard, P.; Rice, S. A., J. Chem. Phys., 90, 2242 (1989)
[12] Gaspard, P.; Rice, S. A., J. Chem. Phys., 90, 2255 (1989)
[13] Rankin, C. C.; Miller, W. H., J. Chem. Phys., 55, 3150 (1971)
[14] Noid, D. W.; Gray, S. K.; Rice, S. A., J. Chem. Phys., 84, 2649 (1986)
[15] Dünneweber, W., Phys. Rev. Lett., 61, 927 (1988)
[16] Glaesner, A., Phys. Lett. B, 169, 153 (1986)
[17] Brink, D. M.; Dietrich, K., Z. Physik A, 326, 7 (1987)
[18] Bonetti, R.; Hussein, M. S., Phys. Rev. Lett., 57, 105 (1986)
[19] Eckhardt, B., Physica D, 33, 89 (1988) · Zbl 0669.58050
[20] U. Smilansky, The classical and quantum theory of chaotic scattering, in: Proceedings of the 1989 Les Houches Summer School on Chaos and Quantum Physics, to be published.; U. Smilansky, The classical and quantum theory of chaotic scattering, in: Proceedings of the 1989 Les Houches Summer School on Chaos and Quantum Physics, to be published. · Zbl 0753.58037
[21] Tél, T., Phys. Rev. A, 36, 1502 (1987)
[22] Blümel, R.; Smilansky, U., Phys. Rev. Lett., 64, 241 (1990) · Zbl 1050.82528
[23] Beenakker, C. W.J.; van Houten, H., Phys. Rev. Lett., 63, 1857 (1989)
[24] Miller, W. H., Adv. Chem. Phys., 9, 48 (1974)
[25] Marcus, R. A., J. Chem. Phys., 54, 3965 (1971)
[26] Blümel, R.; Smilansky, U., Phys. Rev. Lett., 60, 477 (1988)
[27] Ericson, T., Phys. Rev. Let., 5, 430 (1960)
[28] Ericson, T., Ann. Phys., 23, 390 (1963)
[29] Pereyra, P.; Mello, P. A., J. Phys. A, 16, 237 (1983) · Zbl 0508.60088
[30] Milo, private communication.; Milo, private communication.
[31] Jalabert, R. A.; Baranger, H. U.; Stone, A. D., Yale preprint (1990)
[32] Wardlaw, D. M.; Jaworski, W., J. Phys. A, 22, 3561 (1989) · Zbl 0698.58050
[33] Amrein, W. O.; Cibils, M. B., Helvet. Phys. Acta, 60, 481 (1987)
[34] Goldberger, M. L.; Watson, K. M., Collision Theory (1964), Wiley: Wiley New York · Zbl 0131.43503
[35] Doron, E.; Smilansky, U.; Frenkel, A., Phys. Rev. Lett., 65, 3072 (1990)
[36] Kaveh, M.; Rosenbluth, M.; Edrrei, I.; Freund, I., Phys. Rev. Lett., 57, 2049 (1986)
[37] Akkermans, E.; Maynard, R., J. Phys. (Paris) Lett., 46, L1045 (1985)
[38] Golub, G. H.; van Loan, C. H., Matrix Computations (1983), Johns Hopkins Univ. Press: Johns Hopkins Univ. Press Baltimore, MD · Zbl 0559.65011
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.