Reversals of noise induced flow in a 3-state fluctuating potential
M. Bier
Section of Plastic 
Reconstructive Surgery, Dept. of Surgery
MC6035, University of Chicago, 5841 S. Maryland Avenue, Chicago IL 60637,
USA
We take a periodic, anisotropic, piecewise linear potential like the one below and consider diffusive motion. Every period has the same amount of probability. If the potential doesn't change in time we get a Boltzmann distribution for the probability density as a function of x (see below).
Next we fluctuate between the above potential V(x), a flat potential (V=0) and the inverted potential -V(x). Such an application of three state multiplicative noise can bring about a net flow of probability along the x axis, even though no macroscopic force is ever applied. When parameters of the noise, like speed and flatness, are changed the direction of the flow can change.
This periodic and piecewise linear setup allows for an analytic evaluation of the probability density and the flow. Getting the solution involves a substantial amount of algebra. A more intuitive approach leads to good quantitative estimates and a better understanding of the flux revesals.
We are currently building a device that is based on these principles and separates microscopic particles according to their coefficient of friction. The device operates such that, for any mixture of two kinds of particles, one kind can be made to move to the the left and the other kind to the right.