Stringent Numerical Test of the Poisson Distribution for Finite Quantum   Integrable Hamiltonians
  Using a new 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 cases, 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 to the work of the Berry and Tabor in the semiclassical limit. 
A. Relano (1), J. Dukelsky (2), J. M. G. Gomez (1) and J. Retamosa (1)   ((1) Departamento de Fisica Atomica, Molecular y Nu...