Study of the slow dynamics in a highly supercooled fluid: Superlong-time molecular-dynamics calculation of the generalized susceptibility

Generalized susceptibility χ(q,ω) for binary soft-sphere mixtures is computed for the first time for a frequency range which includes both the α and β peaks in a supercooled fluid phase with a superlongtime (10 × 106 time steps) molecular dynamics simulation. This gives us reliable spectral data in a wide frequency range of over 5 orders of magnitude and at various wave numbers, so that we can discuss without ambiguity the dynamical behavior of both α and β relaxations. The α and β peaks in χ′′(q,ω) are obtained for the first time by molecular dynamics simulation. It is shown that the α peak has a non-Debye-type ω dependence, the β peak is essentially of a Debye type, and a crossover between the α and β peaks manifests itself in the so-called β relaxation.