We numerically study dynamical properties of the one-component Gaussian Core Model in the supercooled states. We find that nucleation is suppressed as density increases. Concomitantly the system exhibits glassy slow dynamics characterized by the two-step and stretched exponential relaxation of the density correlation as well as drastic increase of the relaxation time. It is found that violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than typical model glass formers, implying weaker dynamic heterogeneities. Besides, agreement of simulation data with the prediction of mode-coupling theory is exceptionally good, indicating that the nature of slow dynamics of this ultra-soft particle fluid is mean-field-like. This fact may be understood as the consequences of multiple overlaps of the constituent particles at high densities.

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