DYNAMICS OF A MODEL OF A SUPERSOLID

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 peri odic wave function, which represents a new solid phase with long range phase order, as in superfluids. Properties and characteristics of thi s supersolid are discussed. Although uniform rotation occurs without d issipation, dissipationless flow around an obstacle is not possible. W e show the existence of ''supersolid vortices'' and propose some exper iments to test the theory.