Parametric evolution for a deformed cavity

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

Volumn 63, Issue 4, 2001, Pages

  Cohen, Doron ^a   Barnett, Alex ^a   Heller, Eric J ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; DEFORMATION; EIGENVALUES AND EIGENFUNCTIONS; HAMILTONIANS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; QUANTUM THEORY;

LOCAL DENSITY OF STATE (LDOS); PARAMETRIC EVOLUTION;

CHAOS THEORY;

EID: 0035303701     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.63.046207     Document Type: Article

References (27)

1. The classical approximation for (Formula presented) works well for ergodic eigenstates. As explained later in the text we actually consider the averaged profile. Namely, (Formula presented) is regarded as a function of (Formula presented), and it is averaged over the reference state m. With this procedure the effect of the minority of nonergodic eigenstates can be neglected in the classical limit.
2. The two parametric scales of Wigner’s RMT model correspond to (Formula presented) and (Formula presented) of Table I. Consequently there are three parametric regimes in Wigner’s theory. These are the standard perturbative regime (Formula presented), the Lorentzian regime (Formula presented), and the semi-circle regime (Formula presented). As an artifact of this RMT model, there actually exists a forth regime (Anderson strong localization regime) that in the present context does not have a semiclassical analog.
3. As explained in Ref. 8 the generic hierarchy is (Formula presented). This hierarchy is realized in the classical limit (small (Formula presented) where we have soft walls (see Sec. II). The hard wall limit is nongeneric, and these four parametric scales coincide. In the present paper we assume hard walls unless stated otherwise.
4. G. Casati, B. V. Chirikov, I. Guarneri, and F. M. Izrailev, Phys. Rev. E 48, R1613 (1993);
5. G. CasatiB. V. ChirikovI. GuarneriF. M. IzrailevPhys. Lett. A 223, 430 (1996).
6. V. V. Flambaum, A. A. Gribakina, G. F. Gribakin, and M. G. Kozlov, Phys. Rev. A 50, 267 (1994).
7. G. Casati, B. V. Chirikov, I. Guarneri, and F. M. Izrailev, Phys. Lett. A 223, 430 (1996);
8. F. Borgonovi, I. Guarneri, and F. M. Izrailev, Phys. Rev. E 57, 5291 (1998).
9. E. Heller in Chaos and Quantum Physics, Proceedings of Session LII of the Les-Houches Summer School, edited by A. Voros and M.-J. Giannoni (North-Holland, Amsterdam, 1990).
10. D. Cohen and E. J. Heller, Phys. Rev. Lett. 84, 2841 (2000).
11. C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-photon Interactions: Basic Processes and Applications (Wiley, New York, 1992).
12. E. Wigner, Ann. Math. 62, 548 (1955);
13. Ann. Math.E. Wigner65, 203 (1957).
14. M. Feingold and A. Peres, Phys. Rev. A 34, 591 (1986);
15. M. Feingold, D. Leitner, and M. Wilkinson, Phys. Rev. Lett. 66, 986 (1991);
16. M. Wilkinson, M. Feingold, and D. Leitner, J. Phys. A 24, 175 (1991);
17. M. Feingold, A. Gioletta, F. M. Izrailev, and L. Molinari, Phys. Rev. Lett. 70, 2936 (1993).
18. D. Cohen, Phys. Rev. Lett. 82, 4951 (1999).
19. D. Cohen, in Proceedings of the International School of Physics “Enrico Fermi” Course CXLIII, edited by G. Casati, I. Guarneri, and U. Smilansky (IOS Press, Amsterdam, 2000).
20. D. Cohen, Ann. Phys. (N.Y.) 283, 175 (2000).
21. D. Cohen and T. Kottos, Phys. Rev. E (to be published).
22. M. V. Berry and M. Wilkinson, Proc. R. Soc. London 392, 15 (1984).
23. A. Barnett, D. Cohen, and E. J. Heller, Phys. Rev. Lett. 85, 1412 (2000).
24. A. Barnett, D. Cohen, and E. J. Heller, J. Phys. A (to be published).
25. E. Vergini and M. Saraceno, Phys. Rev. E 52, 2204 (1995);E. Vergini, Ph. D. thesis, Universidad de Buenos Aires, 1995.
26. A. Barnett, Ph.D. thesis, Harvard, 2000.
27. In order to find the average profile we divide the (Formula presented) axis into small bins. We find the average (Formula presented) value in each bin. In order to get (Formula presented) we resample the average profile. The distance between the sampling points is equal to the mean level spacing. We are not interested in features on scale of the mean level spacing. Therefore the transformation from the continuous variable (Formula presented) to the integer variable r should not be considered as problematic.