Wigner--Dyson statistics for a class of integrable models

Details Wigner--Dyson statistics for a class of integrable models Wigner--Dyson statistics for a class of integrable models

2003-06-06

arxiv.org/abs/nlin/0306009v1

Phys. Rev. E, vol 68 (2003) 045201R

Nonlinear Sciences

Chaotic Dynamics

3 pages, 1 figure

Scientific paper

10.1103/PhysRevE.68.045201

We construct an ensemble of second--quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one GOE or GUE statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely the boson number, and thus are integrable. To construct this ensemble we use some ``reverse engineering'' starting from the fact that $n$--bosons in a two--level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an $n$--body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.

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