Positional Order and Diffusion Processes in Particle Systems

Details Positional Order and Diffusion Processes in Particle Systems Positional Order and Diffusion Processes in Particle Systems

2006-04-04

arxiv.org/abs/cond-mat/0604075v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, 4 figures. Submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.74.030201

Nonequilibrium behaviors of positional order are discussed based on diffusion processes in particle systems. With the cumulant expansion method up to the second order, we obtain a relation between the positional order parameter $\Psi$ and the mean square displacement $M$ to be $\Psi \sim \exp(- {\bf K}^2 M /2d)$ with a reciprocal vector ${\bf K}$ and the dimension of the system $d$. On the basis of the relation, the behavior of positional order is predicted to be $\Psi \sim \exp(-{\bf K}^2Dt)$ when the system involves normal diffusion with a diffusion constant $D$. We also find that a diffusion process with swapping positions of particles contributes to higher orders of the cumulants. The swapping diffusion allows particle to diffuse without destroying the positional order while the normal diffusion destroys it.

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