Fluctuation dispersion of transport coefficients in a Bose superfluid

The contribution made by interactions of the hydrodynamic modes to the transport coefficients of a Bose superfluid is investigated. It is shown that the generalized transport coefficients, which depend on the wave vector and the frequency, can be expressed exactly in terms of the elements of the mass operator for the matrix correlation function of the basic hydrodynamic variables. The mode-coupling approximation in the mass operator is used to obtain a system of integral equations for the transport coefficients. Explicit expressions for the fluctuation corrections are obtained in the three-dimensional case. The dispersion of second sound in the neighborhood of the $\lambda$ point is discussed.