Mass separation by ratchets

The uctuation-induced transport of massive Brownian particles is investigated. Analytic approximations for their current in periodic`ratchet'-potential driven additively by the Ornstein-Uhlenbeck noise are in qualitative agreement with the result of numeric simulations. The ability to separate particles with diierent masses in situations with a constant bias is discussed. We consider the one-dimensional motion of a Brownian particle with coordinate x = x(t), mass m, and viscous friction , m x = ? _ x ? V 0 (x) + F + y(t) + p 2D (t) ; (1) in an asymmetric periodic potential (ratchet) V (x) of period L. F stands for an additionaìload force'. Both last expressions in (1) are noisy source terms. Thermal uctuations are modelled by the Gaussian white noise (t). Its intensity D is given due to an Einstein relation by D = k B T == and, hence, the particle performs Brownian motion in a thermal bath with temperature T. Furthermore, we introduce the action of external uctuating forces y(t) on the particle which exposes the system out of equilibrium. We assume y(t) to be an Ornstein-Uhlenbeck-process with zero average and correlation time. The intensity R hy(t)y(0)idt is labelled by Q and is independent of the correlation time. It is convenient to express Q in units of the thermal noise strength D introducing R by Q = R D. Overdamped situations ! 1 of eq.(1) with diierent types of y(t) was the topic of a lot of studies 1,2], recently, pointing in their application to biological systems. A rich material for several physical situations of driving, either by periodic or by stochastic forces y, was investigated in detail (for review see 2]). Also the uctuation induced transport was veriied experimentally 3]. Less well elaborated is the case where inertial eeects of the particles come into play. Only in 4] a complex behaviour of the current for a periodic external force without thermal noise was reported. The inclusion of inertial eeects,