On statistics of the ensemble of oscillators under excitation. I. Classical nonlinear oscillators excited by a weak external force

Abstract

The distribution function is searched out of the Fokker—Planck kinetic equation with the small parameter at higher derivatives. The analytic solution is produced by means of a double successive application of the averaging method. It is shown that an external harmonic force leads to the appearance of excessive population in some regions of phase space, where the vibrational frequency of oscillator is close to the frequency of the external force. The present model shows that laser radiation can stimulate chemical reactions with high activation energy, whereas reactions with low activation energy will not be stimulated.