Particle dynamics and Stochastic Resonance in Periodic potentials

We have studied the dynamics of a particle in a periodically driven underdamped periodic potential. Recent studies have reported the occurrence of Stochastic Resonance (SR) in such systems in the high frequency regime, using input energy per period of external drive as a quantifier. The particle trajectories in these systems can be in two dynamical states characterised by their definite energy and phase relation with the external drive. SR is due to the noise assisted transition of the particles between these two states. We study the role of damping on the occurrence of SR. We show that a driven underdamped periodic system exhibits SR only if the damping is below a particular limit. To explain this we study the syatem in the deterministic regime. The existence of the two dynamical states in the deterministic regime is dependent on the amount of damping and the amplitude od external drive. We also study the input energy distributions and phase difference of the response amplitude with the external drive as afunction of the friction parameter.