Directed current of Brownian ratchet randomly circulating between two thermal sources

We consider a Brownian ratchet system which circulates fast and randomly between two thermal sources with different temperatures. The steady current of the system is evaluated by the Langevin simulations. An analytical expression of the current for fast exchange of the noises is obtained. The feature of temperature-dependent current is discussed. The results show that the current for randomly exchanging two white noises is larger than that of periodically changing temperature under the same parameters