Forced Thermal Ratchets and Stochastic Resonance in Inhomogeneous Underdamped Periodic Potential System

In this work we numerically solve the 1-d Langevin equation to obtain the trajectory of the particles moving in a sinusoidal potential in a medium that offers a periodic damping with a phase difference with respect to the potential. In addition, the system is also driven by a periodic force. In a limited range of the systems parameters, two solutions of the trajectories are obtained. These solutions are of small amplitude and large amplitudes with respect to the force. The occurence of stochastic resonance (SR) in a similar system has been explained as due to the existence of these two solutions. Also, due to the frictional asymmetry, the system also exhibits the phenomenon of ratchet effect (RE). In this work, we attempt to obtain both SR and RE simultaneously in the same domain of parameter space considered.