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Eigenvector statistics for the transitions from the orthogonal to the unitary ensemble

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Zeitschrift für Physik B Condensed Matter

Abstract

A description for the eigenvector statistics of classical chaotic systems with a time reversal destroying part of the Hamilton operator is proposed in closed form. We have checked our form by a numerical simulation of a model system capable to show all intermediate stages between orthogonal and unitary behaviour, and proved the superiority to a chi-square distribution.

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References

  1. Dyson, F.J.: J. Math. Phys.3, 1199 (1962)

    Google Scholar 

  2. Kuś, M., Mostowski, J., Haake, F.: J. Phys. A Math. Gen.21, L 1073 (1988)

    Google Scholar 

  3. Brody, T.A., Flores, J., French, J.B., Mello, P.A., Pandey, A., Wong, S.S.: Rev. Mod. Phys.53, 385 (1981)

    Google Scholar 

  4. French, J.B., Kota, V.K.B., Pandey, A. Tomsovic, S.: Ann. Phys. (NY)181, 198 (1988)

    Google Scholar 

  5. Metha, M.L., Pandey, A.: J. Phys. A Math. Gen.16, 2655 (1983)

    Google Scholar 

  6. Brinkmann, J., Engel, Y.M., Levine, R.D.: Chem. Phys. Lett.137, 441 (1987)

    Google Scholar 

  7. Haake, F., Kuś, M., Scharf, R.: Z. Phys. B — Condensed Matter65, 381 (1987)

    Google Scholar 

  8. Alhassid, Y., Feingold, M.: Phys. Rev. A39, 374 (1989)

    Google Scholar 

  9. McDonald, J.F.: J. Math. Phys.15, 596 (1974)

    Google Scholar 

  10. Rosenzweig, N., Monahan, J.E., Mehta, M.L.: Nucl. Phys. A109, 437 (1968)

    Google Scholar 

  11. Alhassid, Y., Levine, R.D.: Phys. Rev. Lett.57, 2879 (1986)

    Google Scholar 

  12. Haake, F., Życzkowski, K.: Phys. Rev. A42, 1013 (1990)

    Google Scholar 

  13. Abramowitz, M., Stegun, A.: Handbook of mathematical functions. Frankfurt: Deutsch 1984

    Google Scholar 

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Author notes

  1. Karol Życzkowski

    Present address: Instytut Fizyki, Uniwersytet Jagielloński, ul. Reymonta 4, PL-30-059, Kraków, Poland

Authors and Affiliations

  1. Fachbereich Physik, Universitäts-GHS, Universitätsstrasse 5, W-4300, Essen, Federal Republic of Germany

    Karol Życzkowski & Georg Lenz

Authors
  1. Karol Życzkowski
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  2. Georg Lenz
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Życzkowski, K., Lenz, G. Eigenvector statistics for the transitions from the orthogonal to the unitary ensemble. Z. Physik B - Condensed Matter 82, 299–303 (1991). https://doi.org/10.1007/BF01324340

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  • DOI: https://doi.org/10.1007/BF01324340

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