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Superbosonization Formula and its Application to Random Matrix Theory

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Abstract

Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random matrices. We clarify the domain of integration for the supermatrices, and give a demonstration of how the model works by calculating the density of states for an ensemble of almost diagonal matrices. It is also shown how one can reduce the supermatrix model to the conventional sigma model.

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References

  1. Efetov, K.B.: Adv. Phys. 32, 53 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  2. Efetov, K.B.: Supersymmetry in Disorder and Chaos. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  3. Verbaarschot, J.J.M., Weidenmüller, H.A., Zirnbauer, M.R.: Phys. Rep. 129, 367 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  4. Mehta, M.L.: Random Matrices. Academic Press, San Diego (1991)

    MATH  Google Scholar 

  5. Beenakker, C.W.J.: Rev. Mod. Phys. 69, 733 (1997)

    Article  ADS  Google Scholar 

  6. Guhr, T., Müller-Groeling, A., Weidenmüller, H.A.: Phys. Rep. 299, 190 (1998)

    Article  ADS  Google Scholar 

  7. Simons, B.D., Altshuler, B.L.: Phys. Rev. Lett. 70, 4063 (1993)

    Article  ADS  Google Scholar 

  8. Andreev, A.V., Altshuler, B.L.: Phys. Rev. Lett. 75, 902 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  9. Kravtsov, V.E., Mirlin, A.D.: JETP Lett. 60, 656 (1994)

    ADS  Google Scholar 

  10. Mirlin, A.D.: Phys. Rep. 326, 259 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  11. Fyodorov, Y.V., Mirlin, A.D.: Phys. Rev. Lett. 67, 2405 (1991)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. Mirlin, A.D., Fyodorov, Y.V., Dittes, F.M., Quezada, J., Seligman, T.H.: Phys. Rev. E 54, 3221 (1996)

    Article  ADS  Google Scholar 

  13. Janssen, M.: Phys. Rep. 295, 1 (1998)

    Article  Google Scholar 

  14. Kravtsov, V.E., Muttalib, K.A.: Phys. Rev. Lett. 79, 1913 (1997)

    Article  ADS  Google Scholar 

  15. Evers, F., Mirlin, A.D.: Phys. Rev. Lett. 84, 3690 (2000)

    Article  ADS  Google Scholar 

  16. Kravtsov, V.E., Yevtushenko, O., Cuevas, E.: J. Phys. A 39, 2021 (2006)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  17. Yevtushenko, O., Kravtsov, V.E.: J. Phys. A 8265, 36 (2003)

    MathSciNet  Google Scholar 

  18. Yevtushenko, O., Kravtsov, V.E.: Phys. Rev. E 69, 26104 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  19. Yevtushenko, O., Ossipov, A.: J. Phys. A 40, 4691 (2007)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  20. Efetov, K.B., Schwiete, G., Takahashi, K.: Rev. Phys. Lett. 92, 26807 (2004)

    Article  Google Scholar 

  21. Efetov, K.B., Kogan, V.R.: Phys. Rev. B 70, 195326 (2004)

    Article  ADS  Google Scholar 

  22. Lehmann, N., Saher, D., Sokolov, V.V., Sommers, H.J.: Nucl. Phys. A 582, 223 (1995)

    Article  ADS  Google Scholar 

  23. Hackenbroich, G., Weidenmüllerxx, H.A.: Phys. Rev. Lett. 74, 4118 (1995)

    Article  ADS  Google Scholar 

  24. Ossipov, A., Kravtsov, V.E.: Phys. Rev. B 73, 033105 (2006)

    Article  ADS  Google Scholar 

  25. Littelmann, P., Sommers, H.-J., Zirnbauer, M.R.: arXiv:math-ph0707.2929v1

  26. Zirnbauer, M.R.: J. Math. Phys. 37, 4986 (1996)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Mirlin, A.D., Evers, F.: Phys. Rev. B 62, 7920 (2000)

    Article  ADS  Google Scholar 

  28. Ndawana, M.L., Kravtsov, V.E.: J. Phys. A 36, 3639 (2003)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  29. Kamenev, A., Mézard, M.: J. Phys. A 32, 4373 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  30. Kamenev, A., Mézard, M.: Phys. Rev. B 60, 3944 (1999)

    Article  ADS  Google Scholar 

  31. Yurkevich, I.V., Lerner, I.V.: Phys. Rev. B 60, 3955 (1999)

    Article  ADS  Google Scholar 

  32. Zirnbauer, M.R.: arXiv:cond-mat/9903338

  33. Verbaarschot, J.J.M., Zirnbauer, M.R.: J. Phys. A 17, 1093 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  34. Osipov, V.Al., Kanzieper, E.: Phys. Rev. Lett. 99, 050602 (2007)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Physics Division, National Center for Theoretical Sciences, Hsinchu, 300, Taiwan

    J. E. Bunder

  2. Theoretische Physik III, Ruhr-Universität Bochum, 44780, Bochum, Germany

    K. B. Efetov

  3. L.D. Landau Institute for Theoretical Physics, 117940, Moscow, Russia

    K. B. Efetov & V. E. Kravtsov

  4. The Abdus Salam ICTP, Strada Costiera 11, 34100, Trieste, Italy

    V. E. Kravtsov & O. M. Yevtushenko

  5. Institut für Theoretische Physik, Universität zu Köln, 50937, Köln, Germany

    M. R. Zirnbauer

Authors
  1. J. E. Bunder
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  2. K. B. Efetov
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  3. V. E. Kravtsov
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  4. O. M. Yevtushenko
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  5. M. R. Zirnbauer
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Correspondence to M. R. Zirnbauer.

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Bunder, J.E., Efetov, K.B., Kravtsov, V.E. et al. Superbosonization Formula and its Application to Random Matrix Theory. J Stat Phys 129, 809–832 (2007). https://doi.org/10.1007/s10955-007-9405-y

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  • DOI: https://doi.org/10.1007/s10955-007-9405-y

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