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Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians

A. Relano·J. Dukelsky·J. M. G. Gomez·J. Retamosa
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Abstract

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.

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A. Relano, J. Dukelsky, J. M. G. Gomez, J. Retamosa. 2004-05-24. Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians. https://doi.org/10.1103/physreve.70.026208

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