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



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Relaño Pérez, Armando and Dukelsky, J. and Gómez Gómez, José María and Retamosa Granado, Joaquín (2004) Stringent numerical test of the Poisson distribution for finite quantum integrable Hamiltonians. Physical Review E, 70 (2). ISSN 1539-3755

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Official URL: http://dx.doi.org/10.1103/PhysRevE.70.026208


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.

Item Type:Article
Additional Information:

©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.

Uncontrolled Keywords:Spectrum, Systems, Chaos, Fluctuations, Statistics
Subjects:Sciences > Physics > Thermodynamics
ID Code:27789
Deposited On:18 Dec 2014 11:55
Last Modified:18 Dec 2014 11:55

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