Symmetric white noise can induce directed current in ratchets

Symmetric white noise can induce directed current in periodic potentials that lack reflection symmetry ~termed ratchets!. The requirement for this to occur is that the white noise possesses non-Gaussian statistical properties with all its odd numbered cumulant correlation averages vanishing identically. The fluctuationinduced current is elucidated for three types of white noise: ~i! symmetric white Poissonian shot noise with exponentially distributed amplitudes, ~ii! two-state diffusion noise being composed of two thermal Nyquist noise sources that successively are switched on and off by dichotomic noise, and ~iii! randomly flashing Gaussian white noise. Because the latter two noise sources are not composed of independent increments, the resulting ratchet dynamics x(t) is non-Markovian. The current versus white-noise intensity typically exhibits a nonmonotonic dependence with a maximum assumed at a suitably tuned noise level. @S1063-651X~97!06110-2#