Abstract
A theory for the statistical properties of spectra of chaotic Hamiltonian systems with approximate integrals of the motion is presented. Spectral statistics are determined by a random matrix ensemble that depends on a single transition parameter, which is evaluated herein semiclassically for Hamiltonians with a symmetry-breaking perturbation. At finite $\ensuremath{\hbar}$, substantial deviations from results of canonical matrix ensembles are predicted. Application is given to a coupled quartic oscillator Hamiltonian.
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