Communication: Drift velocity of Brownian particle in a periodically tapered tube induced by a time-periodic force with zero mean: Dependence on the force period

We study the drift of a Brownian particle in a periodically tapered tube, induced by a longitudinal time-periodic force of amplitude vertical bar F vertical bar that alternates in sign every half-period. The focus is on the velocity dependence on the force period, which is usually considered not tractable analytically. For large vertical bar F vertical bar we derive an analytical solution that gives the velocity as a function of the amplitude and the period of the force as well as the geometric parameters of the tube. The solution shows how the velocity decreases from its maximum value to zero as the force period decreases from infinity (adiabatic regime) to zero. Our analytical results are in excellent agreement with those obtained from 3D Brownian dynamics simulations. (C) 2011 American Institute of Physics. [doi:10.1063/1.3647873]