Periodically driven underdamped periodic and washboard potential systems: Dynamical states and stochastic resonance

Abstract

We have studied the motion of an underdamped Brownian particle in (i) a bistable periodic potential and (ii) washboard potentials subjected to a sinusoidal external field. The particles are shown to be effectively in two dynamical states of their trajectories with distinct amplitudes and phase relationship with the external drive. These dynamical states are stable with fixed energies at low temperatures, but transitions between them take place as the temperature is increased. The average input energy loss to the environment per period of the drive shows a stochastic resonance (SR) peak as a function of temperature for the underdamped system potentials studied. The occurrence of SR in these systems is explained using the statistics of transitions between the two dynamical states.