Gaussian density fluctuations and mode coupling theory for supercooled liquids

The equations of motion for the density modes of a fluid, derived from Newt ons equations, are written as a linear generalized Langevin equation. The c onstraint imposed by the fluctuation-dissipation theorem is used to derive an exact form for the emory function. The resulting equations, solved under the assumption that the noise, and consequently density fluctuations, of t he liquid are Gaussian distributed, are equivalent to the random phase appr oximation for the static structure factor and to the well-known ideal mode coupling theory (MCT) equations for the dynamics. This finding suggests tha t MCT is a theory of fluid dynamics that becomes exact in a mean-field limi t.