Thermal ratchets driven by Poissonian white shot noise

We investigate the overdamped transport of Brownian particles that are placed in spatially periodic potentials ~without and with reflection symmetry! that are subjected to both Poissonian white shot noise and thermal, i.e., Gaussian, white equilibrium fluctuations. The probability current of the output process, which is shown to obey a second-order ordinary differential equation, is analyzed. The limit of strong Poissonian white shot noise is studied analytically; the resulting current is given in closed form in terms of two quadratures. For general forms of the periodic potential we present asymptotic expansions in terms of the ratio between the thermal and the shot noise intensity. Analytic results are presented for the class of piecewise linear, sawtoothlike ratchet potentials. Under specific conditions, the current exhibits a distinctive nonmonotonic dependence on such parameters as temperature and/or asymmetry of the periodic potential. @S1063-651X~97!06104-7#