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Level Curvature Distribution Beyond Random Matrix Theory

  • V. E. Kravtsov
  • I. V. Yurkevich
  • C. M. Canali
Part of the NATO ASI Series book series (NSSB, volume 370)

Abstract

As first suggested by Edwards and Thouless1, the sensitivity of spectrum {E n} of disordered conductors to a small twist of phase φ in the boundary conditions Ψ(x = 0, ρ) = e i φΨ(x = L, ρ) is widely considered as a powerful tool to probe the space structure of eigenfunctions and to distinguish between the extended and the localized states.

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References

  1. 1.
    J. T. Edwards and D. J. Thouless, J. Phys. C., 802, (1972); D. J. Thouless, Phys. Rep. 13, 93 (1974).Google Scholar
  2. 2.
    B. D. Simons and B. L. Altshuler, Phys. Rev. B. 48, 5422 (1993); A. Szafer and B. L. Altshuler, Phys. Rev. Lett. 70, 587 (1993); B. D. Simons, P. A. Lee and B. L. Altshuler, Phys. Rev. Lett. 70, 4122 (1993).ADSCrossRefGoogle Scholar
  3. 3.
    E. P. Wigner, Proc. Cambridge Philos. Soc. 47, 790 (1951); F. J. Dyson, J. Math. Phys. 3, 140 (1962).ADSMATHCrossRefGoogle Scholar
  4. 4.
    M. L. Mehta, Random matrices (Academic Press, Boston, 1991).MATHGoogle Scholar
  5. 5.
    K. B. Efetov, Adv.Phys. 32, 53 (1983).MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    A. V. Andreev, O. Agam, B. D. Simons, and B. L. Altshuler, Phys. Rev. Lett. 76, 3947 (1996).ADSCrossRefGoogle Scholar
  7. 7.
    J. Zakrewski and D. Delande, Phys. Rev. E. 47, 1650 (1993).ADSCrossRefGoogle Scholar
  8. 8.
    F. von Oppen, Phys. Rev. E. 51, 2647 (1995)ADSCrossRefGoogle Scholar
  9. 9.
    Y. V. Fyodorov and H.-J. Sommers, Phys. Rev. E. 51, R2719 (1995).ADSCrossRefGoogle Scholar
  10. 10.
    C. M. Canali, C. Basu, W. Stephan and V. E. Kravtsov, Phys. Rev. B. 54, 1431 (1996).ADSCrossRefGoogle Scholar
  11. 11.
    M. Titov, D. Braun and Y. V. Fyodorov, cond-mat/9611235.Google Scholar
  12. 12.
    K. Zyczkowski, L. Molinari, and F. M. Izrailev, J. Phys. I France. 4, 1469 (1994).CrossRefGoogle Scholar
  13. 13.
    V. E. Kravtsov and I. V. Yurkevich, Phys. Rev. Lett. 78, 3354 (1997).ADSCrossRefGoogle Scholar
  14. 14.
    I. V. Yurkevich and V. E. Kravtsov, Phys. Rev. Lett., 78, 701 (1997).ADSCrossRefGoogle Scholar
  15. 15.
    V. E. Kravtsov and A. D. Mirlin, Pis’ma Zh. Exp. Teor. Fiz. 60, 645 (1994) [JETP Lett. 60, 656 (1994)].Google Scholar
  16. 16.
    M. Buttiker, Y. Imry, and R. Landauer, Phys. Lett. A. 96, 365 (1983).ADSCrossRefGoogle Scholar
  17. 17.
    B. L. Altshuler, V. E. Kravtsov and I. V. Lerner in Mesoscopic Phenomena in Solids, ed. B. L. Altshuler et al., (Elsevier, Amsterdam 1991), p.449 and references therein.Google Scholar
  18. 18.
    V. I. Falko, K. B. Efetov, Phys. Rev. B. 52, 17413 (1995).ADSCrossRefGoogle Scholar
  19. 19.
    V. E. Kravtsov, Habilitationsschrift, Heidelberg University 1992 (unpublished).Google Scholar
  20. 20.
    B. A. Muzykantskii and D. E. Khmelnitskii, Phys. Rev. B. 51, 5480 (1995).ADSCrossRefGoogle Scholar
  21. 21.
    I. E. Smolyarenko and B. L. Altshuler, cond.-math/9606181 (unpublished).Google Scholar
  22. 22.
    C. Castellani and L. Peliti, J. Phys. A 19, L429 (1986); W. Pook and M. Janssen, Z. Phys. B. 82, 295 (1991).ADSCrossRefGoogle Scholar
  23. 23.
    F. Wegner, Z. Phys. B 36, 209 (1980).ADSCrossRefGoogle Scholar
  24. 24.
    Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. B 51, 13403 (1995).ADSCrossRefGoogle Scholar
  25. 25.
    V. E. Kravtsov and M. R. Zirnbauer, Phys. Rev. B. 46, 4332 (1992).ADSCrossRefGoogle Scholar
  26. 26.
    J. J. Verbaarschot, H. A. Weidenmuller and M. R. Zirnbauer, Phys. Rep. 129, 367 (1985).MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    A. D. Mirlin, Pis’ma Zh. Exp. Teor. Fiz. 62, 583 (1995) [JETP-Lett. 62, 603 (1995)].Google Scholar
  28. 28.
    A. D. Mirlin, Phys. Rev. B. 53, 1186 (1996).ADSCrossRefGoogle Scholar
  29. 29.
    E. Abrahams, P. W. Anderson, D. C Licciardello, and T. V. Ramakrishnan, Phys. Rev. Lett. 42, 673 (1979).ADSCrossRefGoogle Scholar
  30. 30.
    J. T. Chalker, Physica A 167, 253 (1990); B. Huckenstein and L. Schweitzer, Phys. Rev. Lett. 72, 713 (1994).ADSCrossRefGoogle Scholar
  31. 31.
    B. L. Altshuler, V. E. Kravtsov, and I. V. Lerner, Zh. Eksp. Teor. Fiz. 91, 2276 (1986) [Sov. Phys. JETP 64, 1352 (1986)].Google Scholar
  32. 32.
    T Brandes, B. Huckestein and L. Schweitzer, cond-math/9605062; T. Ohtsuki and T. Kawarabayashi, cond-math/9701013 and references therein.Google Scholar
  33. 33.
    R. Klesse and M. Metzler, Phys. Rev. Lett. 79, 721 (1997).ADSCrossRefGoogle Scholar
  34. 34.
    J. T. Chalker and P. D. Coddington, J. Phys. C. 21, 2665 (1988).ADSCrossRefGoogle Scholar
  35. 35.
    P. W. Anderson and P. A. Lee, Prog. Theor. Phys. 69, 212 (1980).MathSciNetCrossRefGoogle Scholar
  36. 36.
    E. Akkermans, J. Math. Phys. 38 1781 (1997).MathSciNetADSMATHCrossRefGoogle Scholar
  37. 37.
    D. Braun, E. Hoffstetter, G. Montambaux and A. MacKinnon, cond-mat/9611059.Google Scholar
  38. 38.
    C. Basu, C. M. Canali, V. E. Kravtsov and I. V. Yurkevich (unpublished).Google Scholar

Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • V. E. Kravtsov
    • 1
    • 2
    • 3
  • I. V. Yurkevich
    • 4
  • C. M. Canali
    • 5
  1. 1.International Centre for Theoretical PhysicsTriesteItaly
  2. 2.Landau Institute for Theoretical PhysicsMoscowRussia
  3. 3.Newton Institute for MathematicsCambridgeUK
  4. 4.School of Physics and AstronomyUniversity of BirminghamEdgbaston, BirminghamUK
  5. 5.Department of Theoretical Physics IUniversity of LundLundSweden

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