Diagrammatic approach for open chaotic systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 61, Issue 2, 2000, Pages 1285-1298

  Agam, Oded ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL CORRELATION; COMPLEX MOLECULES; CORRELATION FUNCTION; MICROWAVE EXPERIMENTS; TIME REVERSAL SYMMETRIES; TWO-POINT FUNCTION; WIGNER REPRESENTATION;

CHAOTIC SYSTEMS;

EID: 4244133253     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.61.1285     Document Type: Article

References (45)

1. R. Schinke, Photodissociation Dynamics (Cambridge University Press, Cambridge, England, 1993).
2. T. Ericsson, Phys. Rev. Lett. 5, 430 (1960)
3. T. EricssonAnn. Phys. (N.Y.) 23, 390 (1963).
4. R. T. Pack, E. A. Butcher, and G. A. Parker, J. Chem. Phys. 99, 9310 (1993).
5. D. Zhang and J. Z. H. Zhang, J. Chem. Phys. 101, 3671 (1994).
6. A. J. Dobbyn, M. Stumpf, H.-M. Keller, and W. L. Hase, J. Chem. Phys. 102, 8 (1995).
7. C. E. Porter, Statistical Theory of Spectra: Fluctuations (Academic Press, New York, 1965).
8. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981).
9. J. J. M. Verbaarschot, H. A. Weidenmüller, and M. R. Zirenbauer, Phys. Rep. 129, 367 (1985).
10. P. A. Mello, P. Pereyra, and T. H. Seligman, Ann. Phys. (N.Y.) 161, 254 (1985).
11. U. Smilansky, in Chaos and Quantum Physics, edited by A. Voros, and J. Zinn-Justin, M.-J. Giannoni (Elsevier, New York, 1990).
12. C. H. Lewenkopf and H. A. Weidenmüller, Ann. Phys. (N.Y.) 212, 53 (1991).
13. Y. V. Fyodorov and H.-J. Sommers, J. Math. Phys. 38, 1918 (1997).
14. A. A. Abrikosov, L. P. Gor’kov, and I. E. Dzyaloshinski, Methods of Quantum Field Theory in Statistical Physics (Dover, New York, 1975).
15. I. L. Aleiner and A. I. Larkin, Chaos, Solitons and Fractals 8, 1179 (1997).
16. O. Agam, B. L. Altshuler, and A. V. Andreev, Phys. Rev. Lett. 75, 4389 (1995).
17. For a review, see B. L. Altshuler and B. D. Simons, in Proceedings of Les Houches Summer School, Session LXI, Mesoscopic Quantum Physics, edited by E. Akkermans, G. Montambaux, J.-L. Pichard, and J. Zinn-Justin (North-Holland, Amsterdam, 1995).
18. D. Ruelle, Phys. Rev. Lett. 56, 405 (1986)
19. D. RuelleJ. Stat. Phys. 44, 281 (1986).
20. M. Pollicot, Ann. Math. 131, 331 (1990).
21. D. J. Thouless, Phys. Rep. 13, 93 (1974).
22. M. L. Mehta, Random Matrices (Academic Press, New York, 1991).
23. Y. V. Fyodorov and Y. Alhassid, Phys. Rev. A 58, R3375 (1998).
24. Y. Alhassid and Y. V. Fyodorov, J. Phys. Chem. 102, 9577 (1998).
25. W. Lu, M. Rose, K. Pance, and S. Sridhar, Phys. Rev. Lett. 82, 5233 (1999).
26. M. V. Berry and K. E. Mount, Rep. Prog. Phys. 35, 315 (1972).
27. M. C. Gutzwiller, Chaos in Classical and Quantum Mechanics (Springer, New York, 1990).
28. M. V. Berry, Proc. R. Soc. London, Ser. A 423, 219 (1989).
29. M. V. Berry, Proc. R. Soc. London, Ser. A 400, 229 (1985).
30. O. Agam, Phys. Rev. B 54, 2607 (1996);and in Supersymmetry and Trace Formulae: Chaos and Disorder (Plenum, New York, 1999), pp. 133–151.
31. M. V. Berry, Philos. Trans. R. Soc. London, Ser. A 287, 237 (1977).
32. The connected part of the correlator of two random variables, say g and f, is defined as (Formula presented).
33. P. Cvitanović, Phys. Rev. Lett. 61, 2729 (1988).
34. P. Gaspard and S. A. Rice, J. Chem. Phys. 90, 2225 (1989)
35. J. Chem. Phys.P. GaspardS. A. Rice90, 2242 (1989)
36. J. Chem. Phys.P. GaspardS. A. Rice90, 2255 (1991)
37. J. Chem. Phys.P. GaspardS. A. Rice91, 3279(E) (1989).
38. P. Gaspard and D. A. Ramirez, Phys. Rev. A 45, 8383 (1992).
39. R. Blümel and U. Smilansky, Phys. Rev. Lett. 60, 477 (1988)
40. R. BlümelU. SmilanskyPhysica D 36, 111 (1989).
41. R. A. Jalabert, H. H. Baranger, and A. D. Stone, Phys. Rev. Lett. 65, 2442 (1990).
42. Y.-C. Lai, R. Blümel, E. Ott, and C. Grebogi, Phys. Rev. Lett. 68, 3491 (1992).
43. E. Doron, U. Smilansky, and A. Frenkel, Phys. Rev. Lett. 65, 3072 (1990).
44. The Ruelle resonances of the four-disk system have been calculated by Gaspard and Ramirez 33 using the cycle expansion. In this calculation, the ratio of the distance between the disks to their radius is 3, while in the experiment 23 it is 4. Nevertheless, these theoretical calculations show that indeed the subleading Ruelle resonance are complex.
45. K. B. Efetov, Adv. Phys. 32, 53 (1983).