The tube wall fluctuation can induce a net current in a periodic tube

We study the transport of Brownian particles moving within a three-dimensional periodic tube in the presence of an elastic wall without any external force. The tube wall can fluctuate between the two states. Reduction of the coordinates may involve the appearance of an entropic barrier and an effective diffusion constant. It is found that the tube wall fluctuation can induce a net current without any external force. The direction of the movement is determined by the sign of the asymmetric parameter of the tube wall. There exists an optimized value of the fluctuation rate (or the ratio of the two fluctuation rates) at which the average velocity takes its maximum value.