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Motivated by recent experimental realization of a Bose-Einstein condensate (BEC) of dipolar molecules, we develop superfluid transport theory for a dissipative BEC to show that a weak uniform two-body loss can induce phase rigidity, leading to superfluid transport of bosons. A generalized f-sum rule is shown to hold for a dissipative superfluid as a consequence of weak U(1) symmetry. It is also demonstrated that dissipation enhances the stability of a molecular BEC with dipolar interactions. Possible experimental situations for measuring the superfluid fraction and the spectral function are discussed.
Li et al. (Thu,) studied this question.