Positional order and diffusion processes in particle systems

The relaxation of a nonequilibrium solid to a fluid is determined by observing the positional order parameter in Monte Carlo simulations, and discussed based on diffusion processes in the hard-particle systems. From the cumulant expansion up to the second order, the relation between the positional order parameter and the mean square displacement ui2 is obtained to be exp (K2ui22d) with a reciprocal vector K and the dimension of the system d. On the basis of this relation, the positional order should decay exponentially as exp (K2 Dt) when the system involves normal diffusion with a diffusion constant D. A diffusion process with swapping positions of particles is also discussed. The swapping of particles contributes to the higher orders of the cumulants, and swapping positions allows particles to diffuse without destroying the positional order while the normal diffusion destroys it.