Energy diffusion of a weakly damped and periodically driven particle in an anharmonic potential well

Abstract

The dynamics of a particle in an anharmonic potential well is studied for the case where the oscillations of the particle are disturbed by the dissipative and random forces caused by a thermal bath and by an external driving force. The former interaction is characterized by a damping coefficient with arbitrary frequency dependence. The damping is assumed to be weak so that the average energy loss of the particle per oscillation period is much less than the energy. Also the energy change per oscillation period due to the external force is assumed to be small compared to the energy, at least for large-amplitude oscillations. Under these weak-coupling conditions the non-Markov process of the position and momentum variables of the particle can be reduced to a Markov process for the energy and phase variables. The Markov process is described by a Fokker-Planck equation, the drift and diffusion coefficients of which are calculated systematically.