Abstract
As mentioned in section 6, when investigating dynamical chaos in classical Hamiltonian systems two convenient concepts are the “nonlinear resonance” (NR) and “interaction (overlapping) of NRs” [57]. Namely, the transition to chaos takes place under conditions of strong interaction of NRs in classical Hamiltonian systems [57]. These concepts also appear to be useful in the investigation of quantum chaos in Hamiltonian systems [63–66,9,15,53]. In this case quantum nonlinear resonances occur (QNR) [63,64]. Under the condition of strongly developed chaos in the classical limit, when an infinite number of primary NRs are overlapped (section 6), the time-scale τ ħ of applicability of the quasiclassical approach can be estimated analytically (see (6.36), (6.37), (6.39)), and is logarithmically small in terms of the quasiclassical parameter κ (6.38).
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