Thermal effects on chaotic directed transport

We study a chaotic ratchet system under the influence of a thermal environment. By direct integration of the Lindblad equation we are able to analyze its behavior for a wide range of couplings with the environment, and for different finite temperatures. We observe that the enhancement of the classical and quantum currents due to temperature depend strongly on the specific properties of the system. This makes difficult to extract universal behaviors. We have also found that there is an analogy between the effects of the classical thermal noise and those of the finite $\hbar$ size. These results open many possibilities for their testing and implementation in kicked BECs and cold atoms experiments.