Correlation Functions of Impedance and Scattering Matrix Elements in Chaotic Absorbing Cavities

• Authors: D Savin , Y Fyodorov , H Sommers
• Languages of publication: EN

Abstracts

EN

Wave scattering in chaotic systems with a uniform energy loss (absorption) is considered. Within the random matrix approach we calculate exactly the energy correlation functions of different matrix elements of impedance or scattering matrices for systems with preserved or broken time-reversal symmetry. The obtained results are valid at any number of arbitrary open scattering channels and arbitrary absorption. Elastic enhancement factors (defined through the ratio of the corresponding variance in reflection to that in transmission) are also discussed.

Keywords

EN

05.45.Mt; 24.60.-k; 42.25.Bs; 03.65.Nk

Discipline

• 03.65.Nk: Scattering theory
• 42.25.Bs: Wave propagation, transmission and absorption[see also 41.20.Jb—in electromagnetism; for propagation in atmosphere, see 42.68.Ay; see also 52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma and 52.38-r Laser-plasma interactions—in plasma physics]
• 24.60.-k: Statistical theory and fluctuations
• 05.45.Mt: Quantum chaos; semiclassical methods

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2006
• Volume: 109
• Issue: 1
• Pages: 53-64

Dates

published

2006-01

received

2005-05-19

Contributors

author

D Savin

• Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany

author

Y Fyodorov

• School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK

author

H Sommers

• Fachbereich Physik, Universität Duisburg-Essen, 45117 Essen, Germany, 45117 Essen, Germany

References

• 1. H.J. Stöckmann, Quantum Chaos: An Introduction, Cambridge University Press, Cambridge 1999
• 2. C.W.J. Beenakker, Rev. Mod. Phys., 69, 731, 1997
• 3. Y. Alhassid, Rev. Mod. Phys., 72, 895, 2000
• 4. E. Doron, U. Smilansky, A. Frenkel, Phys. Rev. Lett., 65, 3072, 1990
• 5. C.H. Lewenkopf, A. Müller, E. Doron, Phys. Rev. A, 45, 2635, 1992
• 6. R. Schäfer, T. Gorin, T.H. Seligman, H.J. Stöckmann, J. Phys. A, Math. Gen., 36, 3289, 2003
• 7. R.A. Méndez-Sánchez, U. Kuhl, M. Barth, C.H. Lewenkopf, H.J. Stöckmann, Phys. Rev. Lett., 91, 174102, 2003
• 8. H. Schanze, H.J. Stöckmann, M. Martínez-Mares, C.H. Lewenkopf, Phys. Rev. E, 71, 016223, 2005
• 9. U. Kuhl, M. Martínez-Mares, R.A. Méndez-Sánchez, H.J. Stöckmann, Phys. Rev. Lett., 94, 144101, 2005
• 10. J. Barthélemy, O. Legrand, F. Mortessagne, Phys. Rev. E, 71, 016205, 2005
• 11. O.I. Lobkis, I.S. Rozhkov, R.L. Weaver, Phys. Rev. Lett., 91, 194101, 2003
• 12. O. Hul, S. Bauch, P. Pakonski, N. Savytskyy, K. Zyczkowski, L. Sirko, Phys. Rev. E, 69, 056205, 2004
• 13. E. Kogan, P.A. Mello, H. Liqun, Phys. Rev. E, 61, R17, 2000
• 14. C.W.J. Beenakker, P.W. Brouwer, Physica E, 9, 463, 2001
• 15. D.V. Savin, H.J. Sommers, Phys. Rev. E, 68, 036211, 2003
• 16. Y.V. Fyodorov, JETP Lett., 78, 250, 2003
• 17. D.V. Savin, H.J. Sommers, Phys. Rev. E, 69, 035201(R), 2004
• 18. I. Rozhkov, Y.V. Fyodorov, R.L. Weaver, Phys. Rev. E, 68, 016204, 2003
• 19. I. Rozhkov, Y.V. Fyodorov, R.L. Weaver, Phys. Rev. E, 69, 036206, 2004
• 20. S. Hemmady, X. Zheng, E. Ott, T.M. Antonsen, S.M. Anlage, Phys. Rev. Lett., 94, 014102, 2005
• 21. S. Hemmady, X. Zheng, T.M. Antonsen, E. Ott, S.M. Anlage, Phys. Rev. E, 71, 056215, 2005
• 22. X. Zheng, T.M. Antonsen, E. Ott, e-print, cond-mat/0408327, 2004
• 23. X. Zheng, T.M. Antonsen, E. Ott, e-print, cond-mat/0408317, 2004
• 24. A.D. Mirlin, Phys. Rep., 326, 259, 2000
• 25. Y.V. Fyodorov, Y. Alhassid, Phys. Rev. A, 58, R3375, 1998
• 26. Y.V. Fyodorov, D.V. Savin, JETP Lett., 80, 725, 2004 [Pis{'}ma v ZhETF, 80, 855, 2004]
• 27. D.V. Savin, H.J. Sommers, Y.V. Fyodorov, e-print, cond-mat/0502359, 2005
• 28. C. Mahaux, H.A. Weidenmüller, Shell-Model Approach to Nuclear Reactions, North-Holland, Amsterdam 1969
• 29. J.J.M. Verbaarschot, H.A. Weidenmüller, M.R. Zirnbauer, Phys. Rep., 129, 367, 1985
• 30. V.V. Sokolov, V.G. Zelevinsky, Nucl. Phys. A, 504, 562, 1989
• 31. C.H. Lewenkopf, H.A. Weidenmüller, Ann. Phys. (N.Y.), 212, 53, 1991
• 32. Y.V. Fyodorov, H.J. Sommers, J. Math. Phys., 38, 1918, 1997
• 33. H.M. Nussenzveig, Causality and Dispersion Relations, Academic Press, New York 1972
• 34. M.L. Mehta, Random Matrices, 2nd ed., Academic Press, New York 1991
• 35. T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep., 299, 189, 1998
• 36. N. Lehmann, D. Saher, V.V. Sokolov, H.J. Sommers, Nucl. Phys. A, 582, 223, 1995
• 37. N. Lehmann, D.V. Savin, V.V. Sokolov, H.J. Sommers, Physica D, 86, 572, 1995
• 38. P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. B, 55, 4695, 1997
• 39. V.V. Sokolov, e-print, cond-mat/0409690, 2004
• 40. J.L. Davy, J. Sound Vib., 115, 145, 1987
• 41. O.I. Lobkis, R.L. Weaver, I.S. Rozhkov, J. Sound Vib., 237, 281, 2000
• 42. Y. Alhassid, R.D. Levine, Phys. Rev. A, 46, 4650, 1992
• 43. Y. Alhassid, Y.V. Fyodorov, J. Phys. Chem. A, 102, 9577, 1998
• 44. X. Zheng, S. Hemmady, T.M. Antonsen, S.M. Anlage, E. Ott, e-print, cond-mat/0504196, 2005
• 45. S. Hemmady, X. Zheng, T.M. Antonsen, E. Ott, S.M. Anlage, e-print, nlin.CD/0506025; Acta Phys. Pol. A, 109, 65, 2006
• 46. J.J.M. Verbaarschot, Ann. Phys. (N.Y.), 168, 368, 1986
• 47. T. Gorin, T.H. Seligman, Phys. Rev. E, 65, 026214, 2002
• 48. K.B. Efetov, Adv. Phys., 32, 53, 1983
• 49. Z. Pluhar, H.A. Weidenmüller, J.A. Zuk, C.H. Lewenkopf, F.J. Wegner, Ann. Phys. (N.Y.), 243, 1, 1995
• 50. K.B. Efetov, Supersymmetry in Disorder and Chaos, Cambridge University Press, Cambridge 1996
• 51. J.A. Zuk, e-print, cond-mat/0412060, 1994
• 52. Y.V. Fyodorov, in: Mesoscopic Quantum Physics, Proc. Les-Houches Summer School, Session LXI, Eds. E. Akkermans, G. Montambaux, J.L. Pichard, J. Zinn-{J}ustin, Elsevier, Amsterdam 1995, p. 493
• 53. F.M. Dittes, Phys. Rep., 339, 215, 2000
• 54. D.V. Savin, V.V. Sokolov, Phys. Rev. E, 56, R4911, 1997
• 55. J.M. Blatt, V.F. Weisskopf, Theoretical Nuclear Physics, Springer-Verlag, Berlin 1979
• 56. W. Hauser, H. Feshbach, Phys. Rev., 87, 366, 1952
• 57. P.A. Moldauer, Phys. Rev. C, 11, 426, 1975
• 58. D. Agassi, H.A. Weidenmüller, G. Mantzouranis, Phys. Rep., 22, 146, 1975
• 59. W.A. Friedman, P.A. Mello, Ann. Phys. (N.Y.), 161, 276, 1985

Identifiers

DOI

10.12693/APhysPolA.109.53