Hybrid nonlinear resonance in Hamiltonian systems

Author: Archil Ugulava
Co-authors: , S. Chkhaidze, G. Mchedlishvili
Keywords: nonlinear resonance, Hamiltonian systems
Annotation:

A nonlinear oscillating system in action-angle variables is characterized by an action-dependent oscillation frequency. During the transition period, the nonlinear oscillating system adjusts to resonance with a certain harmonic of the external electromagnetic field, realizing a nonlinear stationary resonance. Under conditions of nonlinear resonance, the dynamics of the system can be reduced to small deviations of the action from its resonance value. In practice, there is often a case where the action is a fairly large number, and its correction is of the order of several Planck constants. In this case, in the study of nonlinear resonance, a hybrid approach should be applied, following which the classical theory can be used to calculate the resonant action, and the quantum theory can be used to calculate its correction. It is shown that if external radiation has the form of a periodic series of light pulses with a high pulse ratio, which has a polychromatic spectrum, then under conditions of nonlinear hybrid resonance the system dynamics reduces to a slow precessional motion of the average value of the angular momentum. The phenomenon of nonlinear hybrid resonance can be detected using radiation induced by the system at the precession frequency of the average value of the angular momentum. The broadening of this radiation can be determined by the mean-square fluctuations of the same angular momentum.