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Using molecular dynamics simulations for a liquid of identical soft spheres we analyze the relative diffusion constant () and the self diffusion constant where is the interparticle distance and = 2, 3 denotes the dimensionality. We demonstrate that for the periodic boundary conditions, is a function of the system size and the relation: ( = /2) ≅ 2 (), where is the length of the cubic box edge, holds both for = 2 and 3. For = 2 both () and () increase logarithmically with its argument. However, it was found that the diffusive process for large two dimensional systems is very sensitive to perturbations. The sensitivity increases with and even a very low perturbation limits the increase of (). Nevertheless, due to the functional form of () the standard assumption for the Smoluchowski type models of reaction kinetics at three dimensions: () ≈ 2 leads to giant errors if applied for = 2.


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