EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

doi:10.1016/S0252-9602(11)60404-9

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (6): 2323-2342.doi: 10.1016/S0252-9602(11)60404-9

EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

Hongyun Wang

Department of Applied Mathematics and Statistics University of California, Santa Cruz, CA 95064, USA

收稿日期:2011-10-19 出版日期:2011-11-20 发布日期:2011-11-20
基金资助:
This work was partially supported by the US National Science Foundation.

EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

Hongyun Wang

Department of Applied Mathematics and Statistics University of California, Santa Cruz, CA 95064, USA

Received:2011-10-19 Online:2011-11-20 Published:2011-11-20
Supported by:
This work was partially supported by the US National Science Foundation.

摘要/Abstract

摘要：

We study the stochastic motion of a Brownian particle driven by a constant force over a static periodic potential. We show that both the effective diffusion and the effective drag coefficient are mathematically well-defined and we derive analytic expressions for these two quantities. We then investigate the asymptotic behaviors of the effective diffusion and the effective drag coefficient, respectively, for small driving force and for large driving force. In the case of small driving force, the effective diffusion is reduced from its Brownian value by a factor that increases exponentially with the amplitude of the potential. The effective drag coefficient is increased by approximately the same factor. As a result, the Einstein relation between the diffusion coefficient and the drag coefficient is approximately valid when the driving force is small. For moderately large driving force, both the effective diffusion and the effective drag coefficient are increased from their Brownian values, and the Einstein relation breaks down. In the limit of very large driving force, both the effective diffusion and the effective drag coefficient converge to their Brownian values and the Einstein relation is once again valid.

关键词: effective diffusion, effective drag coefficient, Einstein relation, Fokker-Planck equation, probability theory, asymptotic analysis

Abstract:

Key words: effective diffusion, effective drag coefficient, Einstein relation, Fokker-Planck equation, probability theory, asymptotic analysis

中图分类号:

35QXX

Hongyun Wang. EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL[J]. 数学物理学报(英文版), 2011, 31(6): 2323-2342.

Hongyun Wang. EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL[J]. Acta mathematica scientia,Series B, 2011, 31(6): 2323-2342.

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EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

EFFECTIVE DIFFUSION AND EFFECTIVE DRAG COEFFICIENT OF A BROWNIAN PARTICLE IN A PERIODIC POTENTIAL

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