Diffusion coefficients for two-state Brownian motors

Kazuo Sasaki

doi:10.1143/JPSJ.72.2497

Diffusion coefficients for two-state Brownian motors

Kazuo Sasaki

ENG - Applied Physics

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

Abstract

Based on the Fokker-Planck equation, a formula for the effective diffusion coefficient D is derived for a Brownian particle undergoing one-dimensional motion in a two-state Brownian motor (ratchet) in which a spatially periodic, asymmetric potential acting on the particle switches between two states stochastically. It turns out that D is in close relation to the "mobility" μ defined as dυ/dF where υ is the average velocity of the particle and F is the external force acting on it. The formula is applied to specific examples, and it is found that inequality D ≥ μk_BT, with k_B the Boltzmann constant and T the temperature, holds in all the cases investigated. In the light of new results obtained here, an earlier analysis of a biological molecular motor KIF1A based on the "on-off" ratchet is re-examined.

Original language	English
Pages (from-to)	2497-2508
Number of pages	12
Journal	Journal of the Physical Society of Japan
Volume	72
Issue number	10
DOIs	https://doi.org/10.1143/JPSJ.72.2497
Publication status	Published - 2003 Oct 1

Keywords

Brownian motor
Diffusion coefficient
Fokker-Planck equation
Mobility
Ratchet

ASJC Scopus subject areas

Physics and Astronomy(all)

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N2 - Based on the Fokker-Planck equation, a formula for the effective diffusion coefficient D is derived for a Brownian particle undergoing one-dimensional motion in a two-state Brownian motor (ratchet) in which a spatially periodic, asymmetric potential acting on the particle switches between two states stochastically. It turns out that D is in close relation to the "mobility" μ defined as dυ/dF where υ is the average velocity of the particle and F is the external force acting on it. The formula is applied to specific examples, and it is found that inequality D ≥ μkBT, with kB the Boltzmann constant and T the temperature, holds in all the cases investigated. In the light of new results obtained here, an earlier analysis of a biological molecular motor KIF1A based on the "on-off" ratchet is re-examined.

AB - Based on the Fokker-Planck equation, a formula for the effective diffusion coefficient D is derived for a Brownian particle undergoing one-dimensional motion in a two-state Brownian motor (ratchet) in which a spatially periodic, asymmetric potential acting on the particle switches between two states stochastically. It turns out that D is in close relation to the "mobility" μ defined as dυ/dF where υ is the average velocity of the particle and F is the external force acting on it. The formula is applied to specific examples, and it is found that inequality D ≥ μkBT, with kB the Boltzmann constant and T the temperature, holds in all the cases investigated. In the light of new results obtained here, an earlier analysis of a biological molecular motor KIF1A based on the "on-off" ratchet is re-examined.

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KW - Fokker-Planck equation

KW - Mobility

KW - Ratchet

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Diffusion coefficients for two-state Brownian motors

Abstract

Keywords

ASJC Scopus subject areas

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