Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians

Simple item page
dc.contributor.authorRelaño Pérez, Armando
dc.contributor.authorDukelsky, J.
dc.contributor.authorGómez Gómez, José María
dc.contributor.authorRetamosa Granado, Joaquín
dc.date.accessioned2023-06-20T10:49:23Z
dc.date.available2023-06-20T10:49:23Z
dc.date.issued2004-08
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.abstractUsing 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.departmentDepto. de Estructura de la Materia, Física Térmica y Electrónica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.statuspub
dc.eprint.idhttps://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.doi10.1103/PhysRevE.70.026208
dc.identifier.issn1539-3755
dc.identifier.officialurlhttp://dx.doi.org/10.1103/PhysRevE.70.026208
dc.identifier.relatedurlhttp://journals.aps.org/
dc.identifier.urihttps://hdl.handle.net/20.500.14352/51288
dc.issue.number2
dc.journal.titlePhysical Review E
dc.language.isoeng
dc.publisherAmerican Physical Society
dc.relation.projectIDBFM2003-05316-C02-02
dc.relation.projectIDBFM2000-0600
dc.rights.accessRightsopen access
dc.subject.cdu536
dc.subject.keywordSpectrum
dc.subject.keywordSystems
dc.subject.keywordChaos
dc.subject.keywordFluctuations
dc.subject.keywordStatistics
dc.subject.ucmTermodinámica
dc.subject.unesco2213 Termodinámica
dc.titleStringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians
dc.typejournal article
dc.volume.number70
dspace.entity.typePublication
relation.isAuthorOfPublication53fed635-944b-485a-b13a-ea8f9355b7aa
relation.isAuthorOfPublication41cdbde8-9afc-4edf-aa3c-1430d8ad268e
relation.isAuthorOfPublication1d1118d9-569f-4139-988b-921ac5a8407c
relation.isAuthorOfPublication.latestForDiscovery53fed635-944b-485a-b13a-ea8f9355b7aa
Download
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Relano49libre.pdf
Size:
62.67 KB
Format:
Adobe Portable Document Format
downoload Download
Collections
Artículos