We study elementary low energy excitations inside a supersolid. We find that the coupling between the longitudinal lattice vibration mode and the superfluid mode leads to two longitudinal modes (one upper branch and one lower branch) inside the supersolid, while the transverse modes in the supersolid stay the same as those inside a normal solid. We also work out various experimental signatures of these novel elementary excitations by evaluating the Debye-Waller factor, density-density correlation, vortex loop-vertex loop interactions, specific heat and excess entropy from the vacancies per mole.
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