Induced Current in Quantum and Classical Ratchets

In a previous work, we described transport in a classical, externally driven, overdamped ratchet. A transport current arises under two possible conditions: either by increasing the external driving or by adding an optimal amount of noise when the system operates below threshold. In this work, we study the underdamped case. In order to obtain transport it is necessary for the presence of both — a damping mechanism and the lack of symmetries in the potential. Some interesting properties were found: under particular conditions the system could be considered as a mass separation device, and for a specific range of the control parameter, the maximum Lyapunov exponent is reduced when noise is added to the system. We also study analytically and numerically the quantum analog of the same system and explore the conditions to find transport.