| We investigate the phenomenological properties of supersolids---materials that simultaneously display both crystalline order and superfluidity. To explain the recent observation in the torsional oscillator experiments on 4He solid by Kim and Chan we adopt a viscoelastic solid model which is characterized by a frequency-dependent complex shear modulus. In this model, we found that a characteristic time scale which accounts for dissipation in solids grows rapidly as the temperature is reduced, and results in a decrease in the resonant period and a peak in the inverse of Q-factor. We also briefly discuss the possible relation between the torsional oscillator results and the anomalous increase of shear modulus obtained by Day and Beamish.;In a related study, we employ a variational principle together with Galilean covariance and thermodynamic relations to obtain the non-dissipative hydrodynamics and an effective Lagrangian density for supersolids. We study the mode structure of supersolids by calculating the second and fourth sound speeds due to defect propagation. We also calculate the density-density correlation function of a model supersolid using the hydrodynamics of Andreev and Lifshitz, and propose a light scattering experiment to measure the density-density correlation function (which is related to the intensity of scattered light). We find that the central Rayleigh peak of the defect diffusion mode of a normal solid in the density-density correlation function splits into an additional Brillouin doublet due to the longitudinal second sound modes in supersolid phase.;Finally, we study the dynamics of vortices and dislocations in supersolids by using the derived Lagrangian for supersolids. We obtain the effective actions for vortices and dislocations in two-dimensional isotropic supersolids emphasizing the differences from the dynamics in superfluids and solids. As a result we obtain the frequency-dependent inertial masses for slowly moving vortices and dislocations. |
