Quantization and corrections of adiabatic particle transport in a periodic ratchet potential
Abstract
We study the transport of an overdamped particle adiabatically driven by an asymmetric potential which is periodic in both space and time. We develop an adiabatic perturbation theory after transforming the FokkerPlanck equation into a timedependent Hermitian problem, and reveal an analogy with quantum adiabatic particle transport. An analytical expression is obtained for the ensemble average of the particle velocity in terms of the Berry phase of the Bloch states. Its time average is shown to be quantized as a Chern number in the deterministic or tightbinding limit, with exponentially small corrections. In the opposite limit, where the thermal energy dominates the ratchet potential, a formula for the average velocity is also obtained, showing a secondorder dependence on the potential.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 August 2002
 DOI:
 10.1209/epl/i2002001972
 arXiv:
 arXiv:condmat/0201116
 Bibcode:
 2002EL.....59..324S
 Keywords:

 05.40.a;
 72.10.d;
 87.10.+e;
 Fluctuation phenomena random processes noise and Brownian motion;
 Theory of electronic transport;
 scattering mechanisms;
 General theory and mathematical aspects;
 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 8 pages