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A first order phase transition in a model of a superfluid is studied. The transition occurs when the energy gap for rotons decreases below a critical value. The ground state is a purely real, positive, and periodic wave function, which represents a new solid phase with long range phase order, as in superfluids. Properties and characteristics of this supersolid are discussed. Although uniform rotation occurs without dissipation, dissipationless flow around an obstacle is not possible. We show the existence of ``supersolid vortices'' and propose some experiments to test the theory.
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Pomeau et al. (1994) studied this question.
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