Exact analysis of stochastic resonance and directed transport in potential with time-dependent discontinuity

We investigate the one-dimensional diffusion of the particle in piecewise linear potentials in some physically relevant cases. The underlying potential profiles are a W-shaped double well and a periodic array of saw tooth. In both cases the potential is superimposed with step of harmonically oscillating height. Due to the simplified implementation of the driving process we are able to calculate exact (non-linear) time-resolved response represented by the particle mean position and by the particle current. The time-asymptotic and time-averaged response exhibits resonance-like features with respect to the temperature and some other model parameters.