Response functions and superfluid density in a weakly interacting Bose gas with non-quadratic dispersion

Motivated by the experimental search for Bose condensation of quasiparticles in semiconductors, the response functions of a weakly interacting Bose gas, with isotropic but non-quadratic dispersion, are considered. Non-quadratic dispersion modifies the definition of particle current, and leads to modified sum rules for the current-current response function. The effect of these modifications on the Berezhinski-Kosterlitz-Thouless transition is discussed.