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Diffusion Coefficient and Mobility of a Brownian Particle in a Tilted Periodic Potential

Kazuo Sasaki·Satoshi Amari
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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.

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Kazuo Sasaki, Satoshi Amari. 2005-02-01. Diffusion Coefficient and Mobility of a Brownian Particle in a Tilted Periodic Potential. https://doi.org/10.1143/jpsj.74.2226

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