Transition curves for the variance of the nearest neighbor spacing distribution for Poisson to Gaussian orthogonal and unitary ensemble transitions

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

Volumn 60, Issue 3, 1999, Pages 3405-3408

  Kota, V K B ^a   Sumedha, S ^a  

^a PHYSICAL RESEARCH LABORATORY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE;

EID: 0007331228     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.3405     Document Type: Article

References (33)

1. C. E. Porter, Statistical Theories of Spectra: Fluctuations (Academic Press, New York, 1965).
2. T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981).
3. O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
4. S. W. McDonald and A. N. Kaufman, Phys. Rev. Lett. 42, 1189 (1979).
5. M. V. Berry, Proc. R. Soc. London, Ser. A 400, 229 (1985).
6. O. Bohigas, in Chaos and Quantum Physics, Les Houches LII, edited by A. Voros, and J. Zinn-Justin, M.-J. Giannoni (North Holland, Amsterdam, 1991).
7. T. Guhr, A. Muller-Groeling, and H. A. Weidenmuller, Phys. Rep. 299, 189 (1998).
8. J. B. French, V. K. B. Kota, A. Pandey, and S. Tomsovic, Ann. Phys. (N.Y.) 181, 198 (1988).
9. D. M. Leitner, Phys. Rev. E 48, 2536 (1993).
10. A. Pandey, Chaos Solitons Fractals 5, 1275 (1995).
11. T. Guhr, Ann. Phys. (N.Y.) 250, 145 (1996)
12. Ann. Phys. (N.Y.)K. M. Frahm, T. Guhr, and A. Muller-Groeling, 270, 292 (1998)
13. H. Kunz and B. Shapiro, Phys. Rev. E 58, 400 (1998).
14. J. B. French, V. K. B. Kota, A. Pandey, and S. Tomsovic, Ann. Phys. (N.Y.) 181, 235 (1988).
15. H. Alt, C. I. Barbosa, H. D. Graf, T. Guhr, H. L. Harney, R. Hofferbert, H. Rehfeld, and A. Richter, Phys. Rev. Lett. 81, 4847 (1998).
16. T. A. Brody, Lett. Nuovo Cimento 7, 482 (1973).
17. M. V. Berry and M. Robnik, J. Phys. A 17, 2413 (1984).
18. H. Hasegawa, H. J. Mikeska, and H. Frahm, Phys. Rev. A 38, 395 (1988).
19. F. M. Izrailev, J. Phys. A 22, 865 (1989)
20. J. Phys. AG. Casati, F. M. Izrailev, and L. Molinari, 24, 4755 (1991).
21. A. Y. Abul-Magd, J. Phys. A 29, 1 (1996).
22. M. Robnik, J. Dobnikar, and T. Prosen, J. Phys. A 32, 1427 (1999).
23. M. Moshe, H. Neuberger, and B. Shapiro, Phys. Rev. Lett. 73, 1497 (1994).
24. J. B. French and V. K. B. Kota, Annu. Rev. Nucl. Part. Sci. 32, 35 (1982).
25. G. Lenz and F. Haake, Phys. Rev. Lett. 67, 1 (1991)
26. G. Lenz, K. Zyczkowski, and D. Saher, Phys. Rev. A 44, 8043 (1991).
27. E. Caurier, B. Grammaticos, and A. Ramani, J. Phys. A 23, 4903 (1990).
28. V. K. B. Kota, Proc. Symp. Nucl. Phys. A 39, 208 (1997)(Published by Library and Information Services, B. A. R. C., Mumbai, India).
29. The GOE-GUE interpolation is generated by putting (Formula presented) and (Formula presented) in (1) and (2). Then, in terms of the transition parameter (Formula presented), which is the mean square admixing GUE matrix element (Formula presented) divided by two times the square of the mean spacing (Formula presented) of the unperturbed GOE spectrum, the variance of the NNSD is given by (Formula presented)This formula follows directly from Eqs. (17) and (18) of 21. Note that (Formula presented) corresponds to GOE and (Formula presented) gives GUE.
30. S. Tomsovic, Ph. D. thesis, University of Rochester (1986) (unpublished).
31. F. Leyvraz and T. H. Seligman, J. Phys. A 23, 1555 (1990).
32. Handbook of Mathmatical functions, NBS Applied Mathematics Series Vol. 55, edited by M. Abramowtiz and I. A. Stegun (U.S. Govt. Printing Office, Washington, D.C., 1964).
33. H. Alt, C. Dembowski, H. D. Graf, R. Hofferbert, H. Rehfeld, A. Richter, R. Schuhmann, and T. Weiland, Phys. Rev. Lett. 79, 1026 (1997).