title: Wigner-Dyson statistics for a class of integrable models.
abstract: We construct an ensemble of second-quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one Gaussian orthogonal ensemble (GOE) or Gaussian unitary ensemble (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.
authors.affiliation: Centro de Ciencias Físicas, UNAM, Apartado Postal 48-3, 62251 Cuernavaca, Morelos, Mexico.
authors.forename: L
authors.initials: L
authors.lastname: Benet
authors.forename: F
authors.initials: F
authors.lastname: Leyvraz
authors.forename: T H
authors.initials: TH
authors.lastname: Seligman