Characteristic times and current inversion in inertial ratchets with colored thermal noise

We perform a systematical numerical study of the statistical behaviour of a particle immersed in a colored thermal bath moving with friction in a one-dimensional asymmetric and periodic potential and subjected to an external sinusoidal force. To this end, we characterize the problem in terms of a set of three characteristic times and two strength variables that determine the evolution of the system. We solve the corresponding equations of motion by using an iterative approach. We analyze different bath temperature regimes and study the appearance of a current. We also determine whether the evolution is diffusive or not. We find that current inversion is a very robust phenomenon appearing in an oscillatory fashion as a function of the frequency of the time-dependent external force.