Transition of spectral statistics due to overlap of quantum resonance zones

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Abstract
The quasienergy spacing statistics of a particle in an infinite square well perturbed by a monochromatic external field is studied below and above nonlinear quantum resonance overlap. It is found that at small enough perturbations the quasienergies are accurately given by those obtained from a single resonance, integrable Hamiltonian. The quasienergy spacing distribution undergoes a transition from Poissonian toward Wigner-like behavior when quantum resonance zones overlap, indicating the destruction of a quantum local constant of motion.