Molecular dynamics simulation is a useful tool in general to investigate dynamical properties of condensed matters from a microscopic point of view. This is the case for highly supercooled liquids and the liquid-glass transition as well. However, we have to pay special attentions to the length of time as well as the time-mesh size and the system size of the simulations for the study of slow dynamics which governs the relaxation of such particular systems. In this paper, we study the slow dynamics of a highly supercooled fluid by calculating the general susceptibility ξ(q, ω) with both two- and three-dimensional binary soft-sphere models and super-long-time molecular dynamics simulations. It is found that the Cole-Cole analysis clearly distinguishes between the α and β relaxations of supercooled fluid states. A spurious sound-mode peak appearing in ξsn(q, ω) (imaginary part of the general susceptibility) turns out to be located at ω inversely proportional to the length of the simulation cell size and seems to be physically meaningless. This peak may be caused by the periodic boundary conditions used in the present simulation.
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