RT Journal Article
T1 Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians
A1 Relaño Pérez, Armando
A1 Dukelsky, J.
A1 Gómez Gómez, José María
A1 Retamosa Granado, Joaquín
AB 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.
PB American Physical Society
SN 1539-3755
YR 2004
FD 2004-08
LK https://hdl.handle.net/20.500.14352/51288
UL https://hdl.handle.net/20.500.14352/51288
LA eng
NO [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).
NO ©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.
DS Docta Complutense
RD 6 may 2024