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

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.

5 pages, 4 figures, LaTeX (RevTeX 4) Content changed, References added Accepted for publication in PRE

References in corpus (6)

• A Class of Exactly Solvable Pairing Models
• Poisson versus GOE statistics in integrable and non-integrable quantum hamiltonian
• Misleading signatures of quantum chaos
• Alternative Technique for "Complex" Spectra Analysis
• Wigner--Dyson statistics for a class of integrable models
• Chaotic Spectra of Classically Integrable Systems

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