Spectral analysis of quantum-resonance zones, quantum Kolmogorov-Arnold-Moser theorem, and quantum-resonance overlap

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Abstract
The quasienergy spectrum of a particle in an infinite square well perturbed by a monochromatic external field is analyzed in terms of single- and double-resonance Hamiltonians. At small-enough perturbations the quasienergies are accurately given by those obtained from a single-resonance, integrable Hamiltonian. This indicates the existence of a local constant of motion and is a quantum manifestation of the Kolmogorov-Arnold-Moser theorem. At larger perturbations, the quasienergy spacing distributions are Poissonian for the single-resonance Hamiltonian. But for the double-resonance Hamiltonian, the distributions undergo a transition from Poissonian toward Wigner-like behavior when the perturbation is increased from a regime without resonance overlap to a regime with resonance overlap. This indicates the destruction of the local constant of motion through quantum-resonance overlap and its associated quantum number. It is a quantum manifestation of classical-resonance overlap.