A mode coupling theory of higher order time correlation functions

Kawasaki's mode coupling theory [Ann. Phys. 61 (1970) 1] is used to compute time correlation functions of the form 〈Ak0(t0) … Akn(tn)〉, where Ak(t) represents some slowly varying quantity. The Gaussian and Bare Vertex approximations are made, thus yielding extremely simple expressions for these higher order correlation functions. These do not contain any bare transport coefficients and suggest relatively simple tests by which the theory could be checked. Examples relating to light scattering in nonequilibrium systems and the hydrodynamics of simple fluids are presented.