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 fluctuation-induced 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 $x\left(t\right)\mathrm{}$ is non-Markovian. The current versus white-noise intensity typically exhibits a nonmonotonic dependence with a maximum assumed at a suitably tuned noise level.