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We extend the phase field crystal model to accommodate exact atomicconfigurations and vacancies by requiring the order parameter to benon-negative. The resulting theory dictates the number of atoms and describesthe motion of each of them. By solving the dynamical equation of the model,which is a partial differential equation, we are essentially performingmolecular dynamics simulations on diffusive time-scales. To illustrate thisapproach, we calculate the two-point correlation function of a liquid.

Molecular Dynamics on Diffusive Time Scales from the Phase Field Crystal Equation