Publication: Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians
Loading...
Official URL
Full text at PDC
Publication Date
2004-08
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
American Physical Society
Citations
Exportar
Abstract
Using a class of exactly solvable models based on the pairing interaction, we show that it is possible to construct integrable Hamiltonians with a Wigner distribution of nearest-neighbor level spacings. However, these Hamiltonians involve many-body interactions and the addition of a small integrable perturbation very quickly leads the system to a Poisson distribution. Besides this exceptional case, we show that the accumulated distribution of an ensemble of random integrable two-body pairing Hamiltonians is in perfect agreement with the Poisson limit. These numerical results for quantum integrable Hamiltonians provide a further empirical confirmation of the work of Berry and Tabor in the semiclassical limit.
Description
©2004 The American Physical Society. We thank O. Bohigas, P. Leboeuf, and G. Sierra for useful discussions. This work was supported by Grant Nos. BFM2003-05316-C02-02 and BFM2000- 0600.
UCM subjects
Unesco subjects
Keywords
Citation
[1] O. Bohigas, M. J. Giannoni, and C. Schmit, Phys. Rev. Lett. 52, 1 (1984).
[2] M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356, 375 (1977).
[3] St. Weigert, Physica D 56, 107 (1992).
[4] S. Weigert and G. Muller, Chaos, Solitons Fractals 5, 1419 (1995).
[5] W. M. Zhang and D. H. Feng, Phys. Rep. 252, 1 (1995).
[6] D. Poilblanc, T. Ziman, J. Bellissard, F. Mila, and G. Montambaux, Europhys. Lett. 22, 537 (1993).
[7] Y. Alhassid and A. Novoselsky, Phys. Rev. C 45, 1677 (1992).
[8] J. Ch. Angles d’Auriac, J. M. Maillard, and C. M. Viallet, e-print cond-mat/0205101.
[9] V. K. B. Kota, Phys. Rep. 347, 223 (2001).
[10] L. Benet, F. Leyvraz, and T. H. Seligman, Phys. Rev. E 68, 045201(R) (2003).
[11] J. Dukelsky, C. Esebbag, and P. Schuck, Phys. Rev. Lett. 87, 066403 (2001).
[12] P. Crehan, J. Phys. A 28, 6389 (1995).
[13] F. Haake, Quantum Signatures of Chaos (Springer-Verlag, Berlin, 2001).
[14] T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Rev. Mod. Phys. 53, 385 (1981).
[15] F. M. Izrailev, Phys. Rep. 196, 299 (1990).
[16] P. Shukla, Phys. Rev. E 62, 2098 (2000).
[17] G. Casati, B. V. Chirikov, and I. Guarneri, Phys. Rev. Lett. 54, 1350 (1985).
[18] J. M. G. Gómez, R. A. Molina, A. Relaño, and J. Retamosa, Phys. Rev. E 66, 036209 (2002).