Diffusion Coefficient and Mobility of a Brownian Particle in a Tilted Periodic Potential
arXiv:cond-mat/0502017 · doi:10.1143/JPSJ.74.2226
Abstract
The Brownian motion of a particle in a one-dimensional periodic potential subjected to a uniform external force F is studied. Using the formula for the diffusion coefficient D obtained by other authors and an alternative one derived from the Fokker-Planck equation in the present work, D is compared with the differential mobility μ= dv/dF where v is the average velocity of the particle. Analytical and numerical calculations indicate that inequality D \ge μk_{B}T, with k_{B} the Boltzmann constant and T the temperature, holds if the periodic potential is symmetric, while it is violated for asymmetric potentials when F is small but nonzero.
7 pages, 4 figures, submitted to J. Phys. Soc. Jpn