On the Superfluid Fraction of an Arbitrary Many-Body System at T = 0

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I derive a set of sufficient and (barring certain pathologies) necessary conditions for a one-component system with velocity-independent forces to have a super-fluid fraction ρs/ρ equal to unity at zero temperature: In addition to a condition closely related (but not obviously equivalent) to the usual one of off-diagonal long-range order, the ground state should possess unbroken invariance under both spatial translation and time reversal. Some generalizations are made to the case of multicomponent systems.

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