Approach to steady-state current in ratchets

We have studied the approach to the steady state in thermal ratchets looking for signs of the future development of a non-zero current. We have concentrated on the evolution of the statistical root mean square fluctuations of the position of the walker as well as its temporal correlations. We find oscillations and abrupt slope variations in the fluctuations in the position of the ratchet particle and the temporal correlation functions. These effects are due to the fact that the flipping time of the potential is the same order of magnitude as the adiabatic adjustment time for the barrier. We find no oscillations when the flipping time is too low or too high compared with the adiabatic adjustment time.