Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians
dc.contributor.author | Relaño Pérez, Armando | |
dc.contributor.author | Dukelsky, J. | |
dc.contributor.author | Gómez Gómez, José María | |
dc.contributor.author | Retamosa Granado, Joaquín | |
dc.date.accessioned | 2023-06-20T10:49:23Z | |
dc.date.available | 2023-06-20T10:49:23Z | |
dc.date.issued | 2004-08 | |
dc.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. | |
dc.description.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. | |
dc.description.department | Depto. de Estructura de la Materia, Física Térmica y Electrónica | |
dc.description.faculty | Fac. de Ciencias Físicas | |
dc.description.refereed | TRUE | |
dc.description.status | pub | |
dc.eprint.id | https://eprints.ucm.es/id/eprint/27789 | |
dc.identifier.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). | |
dc.identifier.doi | 10.1103/PhysRevE.70.026208 | |
dc.identifier.issn | 1539-3755 | |
dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevE.70.026208 | |
dc.identifier.relatedurl | http://journals.aps.org/ | |
dc.identifier.uri | https://hdl.handle.net/20.500.14352/51288 | |
dc.issue.number | 2 | |
dc.journal.title | Physical Review E | |
dc.language.iso | eng | |
dc.publisher | American Physical Society | |
dc.relation.projectID | BFM2003-05316-C02-02 | |
dc.relation.projectID | BFM2000-0600 | |
dc.rights.accessRights | open access | |
dc.subject.cdu | 536 | |
dc.subject.keyword | Spectrum | |
dc.subject.keyword | Systems | |
dc.subject.keyword | Chaos | |
dc.subject.keyword | Fluctuations | |
dc.subject.keyword | Statistics | |
dc.subject.ucm | Termodinámica | |
dc.subject.unesco | 2213 Termodinámica | |
dc.title | Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians | |
dc.type | journal article | |
dc.volume.number | 70 | |
dspace.entity.type | Publication | |
relation.isAuthorOfPublication | 53fed635-944b-485a-b13a-ea8f9355b7aa | |
relation.isAuthorOfPublication | 41cdbde8-9afc-4edf-aa3c-1430d8ad268e | |
relation.isAuthorOfPublication | 1d1118d9-569f-4139-988b-921ac5a8407c | |
relation.isAuthorOfPublication.latestForDiscovery | 53fed635-944b-485a-b13a-ea8f9355b7aa |
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