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.
Keywords
Cite
@article{arxiv.nlin/0402011,
title = {Stringent Numerical Test of the Poisson Distribution for Finite Quantum Integrable Hamiltonians},
author = {A. Relano and J. Dukelsky and J. M. G. Gomez and J. Retamosa},
journal= {arXiv preprint arXiv:nlin/0402011},
year = {2009}
}
Comments
5 pages, 4 figures, LaTeX (RevTeX 4) Content changed, References added Accepted for publication in PRE