Det-Det correlations for quantum maps: Dual pair and saddle-point analyses

Journal of Mathematical Physics

Volumn 43, Issue 5, 2002, Pages 2214-2240

  Nonnenmacher, S ^a   Zirnbauer, M R ^b  

^a CEA SACLAY   (France)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035981797     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1462417     Document Type: Article

References (33)

1. O. Bohigas, "Random matrix theory and chaotic dynamics," in Chaos et physique quantique (École d'été des Houches, Session LII, 1989), edited by M.J. Giannoni, A. Voros, and J. Zinn-Justin (North Holland, Amsterdam, 1991).
2. M.V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356, 375 (1977).
3. S. Zelditch, Ann. Inst. Fourier 47, 305 (1997).
4. M. Tabor, Physica D 6, 195 (1983).
5. M.V. Berry, Proc. R. Soc. London, Ser. A 400, 229 (1985).
6. F. Haake, M. Kuś, H.-J. Sommers, H. Schomerus, and K. Zyczkowski, J. Phys. A 29, 3641 (1996).
7. S. Kettemann, D. Klaklow, and U. Smilansky, J. Phys. A 30, 3643 (1997).
8. R. Prange, Phys. Rev. Lett. 78, 2280 (1997).
9. E. Bogomolny, F. Leyvraz, and C. Schmit, Commun. Math. Phys. 176, 577 (1996).
10. J.P. Keating and F. Mezzadri, Nonlinearity 13, 747 (2000).
11. J. Marklof, "The Berry-Tabor conjecture," in Proceedings of the 3rd European Congress of Mathematics, Barcelona 2000 (Birkhäuser, Basel, 2001).
12. M.R. Zirnbauer, J. Phys. A 29, 7113 (1996).
13. E.B. Bogomolny and J.P. Keating, Phys. Rev. Lett. 77, 1472 (1996).
14. K.B. Efetov, Adv. Phys. 32, 53 (1983).
15. A.V. Andreev, B.D. Simons, O. Agam, and B.L. Altshuler, Nucl. Phys. B 482, 536 (1996).
16. B.A. Muzykantskii and D.E. Khmel'nitskii, JETP Lett. 62, 76 (1995).
17. A. Altland, C.R. Offer, and B.D. Simons, "Quantum Chaos: Lessons from Disordered Metals," in Supersymmetry and Trace Formulae, Chaos and Disorder, edited by I.V. Lerner, J.P. Keating, and D.E. Khmel'nitskii (Kluwer Academic/ Plenum, Dordrecht, 1999).
18. D. Taras-Semchuk and K.B. Efetov, Phys. Rev. B 64, 115301 (2001).
19. I.V. Gornyi and A.D. Mirlin, "Wave function correlations on the ballistic scale: Exploring quantum chaos by quantum disorder," cond-mat/0105103.
20. M.R. Zirnbauer, "Pair correlations of Quantum Chaotic maps from Supersymmetry," in Supersymmetry and Trace Formulae, Chaos and Disorder, edited by I.V. Lerner, J.P. Keating, and D.E. Khmel'nitskii (Kluwer Academic/Plenum, Dordrecht, 1999).
21. E. Bogomolny, O. Bohigas, and P. Lebœuf, J. Stat. Phys. 85, 639 (1996).
22. R. Howe, Trans. Am. Math. Soc. 313, 539 (1989).
23. H. Weyl, The Classical Groups: Their Invariants and Representations (Princeton University Press, Princeton, NJ, 1946).
24. A.M. Perelomov, Generalized Coherent States and their Applications (Springer, New York, 1986).
25. A.V. Andreev and B.L. Altshuler, Phys. Rev. Lett. 75, 902 (1995).
26. A. Knapp, Representation Theory of Semisimple Groups (Princeton University Press, Princeton, NJ, 1986).
27. M. Stone, Nucl. Phys. B 314, 557 (1989).
28. J. Milnor, Morse Theory, (Princeton University Press, Princeton, NJ, 1963).
29. J. Leray, C.R. Acad. Sci. Paris 228, 1902 (1949).
30. C. Manderfeld, J. Weber, and F. Haake, "Classical versus Quantum Time Evolution of Densities at Limited Phase-Space Resolution," nlin.CD/0107020.
31. S. Fishman, "Wave Functions, Wigner Functions and Green Functions of Chaotic Systems," in Supersymmetry and Trace Formulae, Chaos and Disorder, edited by I.V. Lerner, J.P. Keating, and D.E. Khmel'nitskii (Kluwer Academic/Plenum, Dordrecht, 1999).
32. D. Ruelle, Phys. Rev. Lett. 56, 405 (1986).
33. L.K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains (American Mathematical Society, Providence, RI, 1963).