Europhys. Lett., 59 (3) , pp. 324-329 (2002)
Quantization and corrections of adiabatic particle transport in a periodic ratchet potentialY. Shi1 and Q. Niu2, 3
1 Theory of Condensed Matter, Cavendish Laboratory, University of Cambridge Cambridge CB3 0HE, UK
2 Department of Physics, University of Texas - Austin, TX 78712, USA
3 ICQS, Chinese Academy of Sciences - Beijing 100080, PRC
(Received 7 January 2002; accepted 13 May 2002)
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 Fokker-Planck equation into a time-dependent 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 tight-binding 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 second-order dependence on the potential.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
72.10.-d - Theory of electronic transport; scattering mechanisms.
87.10.+e - Biological and medical aspects: General theory and mathematical aspects.
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