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Chaos and order in second-harmonic generation: Cumulant approach.

We analyze some aspects of the cumulant method for second-harmonic generation of light in the context of the numerical results of Schack and Schenzle [Phys. Rev. A 41, 3847 (1990)] and earlier papers. The cumulant method can be useful in studies of the modifications introduced by quantum mechanics into classical systems which manifest chaotic oscillations. This problem is frequently referred to as ``quantum chaos.''