  In this paper we study the transient dynamics of a Bose superfluid subsequent
to an interaction quench. Essential for equilibration is a source of
dissipation which we include following the approach of Caldeira and Leggett.
Here we solve the equations of motion exactly by integrating out an
environmental bath. We thereby derive precisely the time dependent density
correlation functions with the appropriate analytic and asymptotic properties.
The resulting structure factor exhibits the expected damping and thereby
differs from that of strict Bogoliubov theory. These damped sound modes, which
reflect the physics beyond mean field approaches, are characterized and the
structure factors are found to compare favorably with experiment.
