Sum rules for density and particle excitations in Bose superfluids

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Abstract
Various sum rules for the density and particle operators are derived and discussed. We investigate in detail the properties of the particle state, the natural counterpart of the Feynman state describing collective density excitations. An explicit expression for the energy of the particle state is derived in terms of the interatomic potential, the two-body half-diagonal density, and the momentum distribution. Sum rules accounting for the coupling between particle and density excitations are also derived and the role of the Bose-Einstein condensation explicitly pointed out. Finally we discuss the separate contribution to the various sum rules arising from one-phonon and multiparticle excitations.