Regensburg 2010 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 7: Stochastic processes, brownian motion, and transport
DY 7.3: Talk
Tuesday, March 23, 2010, 10:15–10:30, H46
Semiclassical treatment of a Brownian ratchet using the quantum Smoluchowski equation — •Liam Cleary1, William T. Coffey1, Yuri P. Kalmykov2, and Serguey V. Titov3 — 1Trinity College Dublin, Ireland — 2Université de Perpignan, France — 3Russian Academy of Sciences, Russia
Quantum effects in the noninertial Brownian motion of a particle in a one-dimensional ratchet potential are treated in the high temperature and weak bath-particle coupling limit by solving a quantum Smoluchowski equation for the time evolution of the Wigner function in configuration space. In particular, an analytical expression for the stationary average drift velocity for constant driving forces is presented including quantum corrections to any order in Planck’s constant. The corresponding frequency response is determined using continued fractions in both the linear approximation holding for small ac driving amplitude and in the nonlinear regime for arbitrary driving amplitude exhibiting pronounced ac induced frequency dependence of the dc component of the average drift velocity. Moreover, Shapiro steps are apparent in the dc characteristics for strong ac driving just as in the dc current-voltage characteristics of a point Josephson junction.