Dynamical chaos in the highly excited states of a quantum Daffing oscillator in an external harmonic field

The energy spectrum of the highly excited states of a quantum Daffing oscillator is considered. It is shown that the energy levels satisfy E_n>E_n+1 and E_n -F²/8², when n , where F² and are the intensity and frequency of the external field. It is suggested that this property of the spectrum is the quantum manifestation of a stochastic attractor in the classical nonlinear limit. This property also takes place for large F².Omsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 90–94, March. 1993.