General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

Details General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems General technique of calculating drift velocity and diffusion coefficient in arbitrary periodic systems

1999-09-14

arxiv.org/abs/cond-mat/9909204v1

J. Phys. A: Math. Gen. 32, 7637-7651 (1999)

Physics

Condensed Matter

Statistical Mechanics

12 pages + 2 figures, RevTeX. Submitted to J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/32/44/303

We develop a practical method of computing the stationary drift velocity V and the diffusion coefficient D of a particle (or a few particles) in a periodic system with arbitrary transition rates. We solve this problem both in a physically relevant continuous-time approach as well as for models with discrete-time kinetics, which are often used in computer simulations. We show that both approaches yield the same value of the drift, but the difference between the diffusion coefficients obtained in each of them equals V*V/2. Generalization to spaces of arbitrary dimension and several applications of the method are also presented.

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