Quasiparticle Excitations, Bose Condensation, and the f-Sum Rule.

In a Bose fiuid having a condensate, the density response has two components. One is associated with exciting single quasiparticles out of the condensate and the second is the usual two-body density response involving states above the condensate appearing in any fiuid. We derive the contribution of each component to the f-sum rule. The single quasiparticle contribution is proportional to the condensate function np(T) at all wave vectors Q. This simple sum rule is analogous to the Ambegaokar, Conway, and Baym sum rule giving the one-phonon contribution to the f-sum rule in solids. It is very useful in interpreting neutron scattering measurements of superfluid "He.