Relaño Pérez, ArmandoDukelsky, J.Gómez Gómez, José MaríaRetamosa Granado, Joaquín2023-06-202023-06-202004-081539-375510.1103/PhysRevE.70.026208https://hdl.handle.net/20.500.14352/51288©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.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.engjournal articlehttp://dx.doi.org/10.1103/PhysRevE.70.026208http://journals.aps.org/open access536SpectrumSystemsChaosFluctuationsStatisticsTermodinámica2213 Termodinámica