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Manifestations of Chaos in Quantum Scattering Processes

  • Linda E. Reichl
Part of the Institute for Nonlinear Science book series (INLS)

Abstract

In the late 1970s, the field of “quantum chaos” underwent a transformation when two seemingly different branches of physics, random matrix theory and chaos theory, merged. The motivating force behind the development of random matrix theory (RMT) as a tool to analyze quantum processes was the inability of the nuclear shell model to describe and classify nuclear scattering states at intermediate energies. Contact between random matrix theory and chaos theory occurred when numerical studies of the statistical properties of the quantized chaotic billiards showed agreement with some nuclear scattering data (see, for example, [McDonald and Kaufman 1979]). This led to the realization that one might see signatures of chaos in nuclear scattering data that involved moderately high-energy nuclear states and opened new directions for the application of quantum chaos theory in open quantum systems.

Keywords

Wave Packet Random Matrix Theory Reaction Region Open Quantum System Hard Wall 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Akguc, G. and Reichl, L.E. (2001): Phys. Rev. E 64 56221.ADSCrossRefGoogle Scholar
  2. Akguc, G. and Reichl, L.E. (2003): Phys. Rev. E 67 46,202.Google Scholar
  3. Alhassid, Y. (1997): Rev. Mod. Phys. 69 731.CrossRefGoogle Scholar
  4. Baranger, H.U. and Mello, P.A. (1994): Phys. Rev. Lett. 73 142.ADSCrossRefGoogle Scholar
  5. Baranger, H.U. and Stone, A.D. (1989): Phys. Rev. B 40 8169.ADSCrossRefGoogle Scholar
  6. Beenakker, C.W.J. (2000): Rev. Mod. Phys. 72 895.CrossRefGoogle Scholar
  7. Bloch, C. (1957): Nuc. Phys. 4 503.MATHCrossRefGoogle Scholar
  8. Böhm, D. (1950): Quantum Theory (Prentice-Hall, Inc., Englewood Cliffs, N.J.), p. 260.Google Scholar
  9. Brody, T.A., Flores, J., French J.B., Mello, P.A., Pandey, A., and Wong, S.S.M. (1981): Rev. Mod. Phys. 53 385.MathSciNetADSCrossRefGoogle Scholar
  10. Brouwer, P.W. (1995): Phys. Rev. B 51 16878.ADSCrossRefGoogle Scholar
  11. Brouwer, P.W., Frahm, K.M., and Beenakker, C.W.J. (1997): Phys. Rev. Lett. 78 4737.ADSCrossRefGoogle Scholar
  12. Buttiker, M. (1988): IBM J. Res. Dev. 32 306.MathSciNetCrossRefGoogle Scholar
  13. Camarda, H.S. and Georgopulos, P.D. (1983): Phys. Rev. Lett 50 492.ADSCrossRefGoogle Scholar
  14. Chang, A.M., Baranger, H.U., Pfeiffer, L.N., and West, K.W. (1994): Phys. Rev. Lett. 73 2111.ADSCrossRefGoogle Scholar
  15. Chinnery, P.A. and Humphrey, V.F. (1996): Phys. Rev. E 53 272.ADSCrossRefGoogle Scholar
  16. Chinnery, P.A. and Humphrey, V.F. (1997): J. Acoust. Soc. Am. 101 250.ADSCrossRefGoogle Scholar
  17. Dyson, F.J. (1962): J. Math. Phys. 3 140.MathSciNetADSMATHCrossRefGoogle Scholar
  18. Economou, E.N. (1983): Green’s Functions in Mathematical Physics (Springer-Verlag, Berlin).CrossRefGoogle Scholar
  19. Eisenbud, L. (1948): Ph.D. Dissertation, June 1948 (unpublished).Google Scholar
  20. Ellegaard, C, Guhr, T., Lindemann, K., Lorensen, H.Q., Nygard, J., and Oxborrow, M. (1995): Phys. Rev. Lett. 75 1546.ADSCrossRefGoogle Scholar
  21. Ellegaard, C, Guhr, T., Lindemann, K., Nygard, J., and Oxborrow, M. (1996): Phys. Rev. Lett. 77 4918.ADSCrossRefGoogle Scholar
  22. Feshbach, H. (1962): Ann. Phys. 19 287.MathSciNetADSMATHCrossRefGoogle Scholar
  23. Fisher, D.S. and Lee, P.A., (1981): Phys. Rev. B 23 6851.MathSciNetADSCrossRefGoogle Scholar
  24. Fyodorov, Y.V. and Sommers, H.-J., (1997): J. Math. Phys. 38 1918.MathSciNetADSMATHCrossRefGoogle Scholar
  25. Garg, J.B., Rainwater, J., Petersen, J.S., and Havens, W.W. (1964): Phys. Rev. B 134 985.ADSCrossRefGoogle Scholar
  26. Gopar, V.A., Mello, P.A., and Buttiker, M. (1996): Phys. Rev. Lett. 77 3005.ADSCrossRefGoogle Scholar
  27. Guhr, T., Muller-Groeling, A., and Weidenmuller, H. (1998): Phys. Rep. 299 189.MathSciNetADSCrossRefGoogle Scholar
  28. Haake, F. (2001): Quantum Signatures of Chaos, 2nd Edition (Springer Verlag, Berlin).MATHCrossRefGoogle Scholar
  29. Hacken, G., Werbin, R., and Rainwater, J. (1978): Phys. Rev. C 17 43.ADSCrossRefGoogle Scholar
  30. Haller, E., Koppel, H., and Cederbaum, L.S. (1983): Chem. Phys. Lett. 101 215.ADSCrossRefGoogle Scholar
  31. Haq, R.U., Pandey, A., and Bohigas, O. (1982): Phys. Rev. Lett. 48 1086.ADSCrossRefGoogle Scholar
  32. Hua, L.K. (1963): Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (American Mathematical Society, Providence).Google Scholar
  33. Jalabert, R.A., Baranger, H.U., and Stone, A.D. (1990): Phys. Rev. Lett. 65 2442.ADSCrossRefGoogle Scholar
  34. Jensen, R.V. (1991): Chaos 1 101.MathSciNetADSMATHCrossRefGoogle Scholar
  35. Jung, C. and Seligman, T.H. (1997): Phys. Rep. 285 77.MathSciNetADSCrossRefGoogle Scholar
  36. Kapur, P.L. and Peierls, R. (1938): Proc. Roy. Soc. London A 166 227.ADSGoogle Scholar
  37. Ketzmerick, R. (1996): Phys. Rev. B 54 10841.ADSCrossRefGoogle Scholar
  38. Krieger, T.J. (1967): Ann. Phys. 42 375.ADSCrossRefGoogle Scholar
  39. Landauer, R. (1957): IBM J. Res. Dev. 1 223.MathSciNetCrossRefGoogle Scholar
  40. Lane, A.M. and Thomas, R.G. (1958): Rev. Mod. Phys. 30 257.MathSciNetADSCrossRefGoogle Scholar
  41. Lewenkopf, C. and Weidenmuller, H.A. (1991): Ann. Phys. N.Y. 212 53.MathSciNetADSMATHCrossRefGoogle Scholar
  42. Liou, H.I., Camarda, H.S., Wynchank, S., Slagowitz, M., Hacken, G., Rahn, F., and Rainwater, J. (1972): Phys. Rev. C 5 974.ADSCrossRefGoogle Scholar
  43. Lopez, G., Mello, P.A., and Seligman, T.H. (1981): Z. Phys. A — Atoms and Nuclei 301 351.ADSCrossRefGoogle Scholar
  44. Luna-Acosta, G.A., Mendez-Bermundez, J.A., Seba, P., and Pichugin, K.N. (2002): Phys. Rev. E 65 46605.ADSCrossRefGoogle Scholar
  45. Marcus, C.M., Rimberg, A.J., Westervelt, R.M., Hopkins, P.F., and Gossard, A.C. (1992): Phys. Rev. Lett. 69 506.ADSCrossRefGoogle Scholar
  46. Marcus, CM., Westervelt, R.M., Hopkins, P.F., and Gossard, A.C. (1993): Phys. Rev. B 48 2460.ADSCrossRefGoogle Scholar
  47. Martin, W.C., Zalubas, R., and Hagan, L. (1978): Atomic Energy LevelsThe Rare Earth Elements, U.S. National Bureau of Standards, National Standards Reference Data Series—60 (U.S. GPO, Washington, D.C.).Google Scholar
  48. Mello, P.A. and Baranger, H.U. (1999): Waves Random Media 9 105.ADSMATHCrossRefGoogle Scholar
  49. Mello, P.A., Pereyra, P., and Seligman, T.H. (1985): Ann. Phys. N.Y. 161 254.MathSciNetADSCrossRefGoogle Scholar
  50. Mello, P.A. and Seligman, T.H. (1980): Nucl. Phys. A 344 489.ADSCrossRefGoogle Scholar
  51. Mendez-Bermundez, J.A., Luna-Acosta, G.A., Seba, P., and Pichugin, K.N. (2002): Phys. Rev. E 66 46207.ADSCrossRefGoogle Scholar
  52. Merzbacher, E. (1970): Quantum Mechanics (John Wiley & Sons, New York)Google Scholar
  53. Mucciolo, E.R., Jalabert, R.A., and Pichard, J.-L. (1997): J. Phys.: I (France) 7 1267.CrossRefGoogle Scholar
  54. Na, K. and Reichl, L.E. (1998): J. Stat. Phys. 92 519.MATHCrossRefGoogle Scholar
  55. Okolowicz, J., Ploszajczak, M., and Rotter, I. (2003): Phys. Rep. 374 271.MathSciNetADSMATHCrossRefGoogle Scholar
  56. Pavlov, B.S. (1984): Theor.Math. Phys. 59 544.CrossRefGoogle Scholar
  57. Pavlov, B.S. (1987): Russ. Math. Surv. 42 127.MATHCrossRefGoogle Scholar
  58. Persson, E., Pichugin, K., Rotter, L, and Seba, P. (1998): Phys. Rev. E 58 8001.ADSCrossRefGoogle Scholar
  59. Persson, E., Rotter, L, Stöckmann, H-J., and Barth, M. (2000): Phys. Rev. Lett. 85 2478.ADSCrossRefGoogle Scholar
  60. Porter, C.E. (1965): Statistical Theories of Spectra: Fluctuations (Academic Press, New York).Google Scholar
  61. Prochnow, N.H., Newson, H.W., Bilpuch, E.G., and Mitchell, G.E. (1972): Nucl. Phys. A 194 353.ADSCrossRefGoogle Scholar
  62. Reichl, L.E. and Akguc, G. (2001): Found. Phys. 31 243.CrossRefGoogle Scholar
  63. Rotter, I. (2001): Phys. Rev. E 64 36213.ADSCrossRefGoogle Scholar
  64. Rotter, I., Persson, E., Pichugin, K., and Seba, P. (2000): Phys. Rev. E 62 450.ADSCrossRefGoogle Scholar
  65. Savin, D.V., Fyodorov, Y.V., and Sommers, H.-J. (2001): Phys. Rev. E 63 35202.ADSCrossRefGoogle Scholar
  66. Smalley, R.E., Wharton, L., and Levy, D.H. (1983): J. Chem. Phys. 63 4977.ADSCrossRefGoogle Scholar
  67. Smith, F.T. (1960): Phys. Rev. 118 349.MathSciNetADSMATHCrossRefGoogle Scholar
  68. Sridhar, S. and Kudrolli, A. (1994): Phys. Rev. Lett. 72 2175.ADSCrossRefGoogle Scholar
  69. Stöckmann, H.-J., Persson, E., Kim, Y.-H., Barth, M., Kuhl, U., and Rotter, I. (2002): Phys. Rev. E 65 66211.ADSCrossRefGoogle Scholar
  70. Verbaarschot, J.J.M. (1986): Ann. Phys. 168 368.ADSCrossRefGoogle Scholar
  71. Verbaarschot, J.J.M., Weidenmuller, H.A., and Zirnbauer, M.R. (1985): Phys. Rep. 129 367.MathSciNetADSCrossRefGoogle Scholar
  72. Weaver, R.L. (1989): J. Acoust. Soc. Am. 85 1005.ADSCrossRefGoogle Scholar
  73. Wigner, E.P. and Eisenbud, L.E. (1949): Phys. Rev. 72 29.ADSCrossRefGoogle Scholar
  74. Wigner, E.P. (1955): Phys. Rev. 98 145.MathSciNetADSMATHCrossRefGoogle Scholar
  75. Wigner, E.P. (1959): Conference on Neutron Physics by Time of Flight, Gatlinburg, Tennessee, November 1956, Oak Ridge Natl. Lab. Rept. ORNL-2309, p.67. Reprinted in [Porter 1965], p. 188.Google Scholar
  76. Wigner, E.P. (1967): SIAM Rev. 9 1.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Linda E. Reichl
    • 1
  1. 1.Department of Physics and Center for Statistical Mechanics and Complex SystemsUniversity of Texas at AustinAustinUSA

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