Gaussian density fluctuations and mode coupling theory for supercooled liquids

The equations of motion for the density modes of a fluid, derived from Newton's equations, are written as a linear generalized Langevin equation. The constraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the memory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of the liquid are Gaussian distributed, are equivalent to the random phase approximation for the static structure factor and to the well-known ideal mode coupling theory (MCT) equations for the dynamics. This finding suggests that MCT is a theory of fluid dynamics that becomes exact in a mean-field limit.