Andreev-Lifshitz supersolid hydrodynamics including the diffusive mode
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We have reexamined the Andreev-Lifshitz theory of supersolids. This theory implicitly neglects uniform bulk processes that change the vacancy number and assumes an internal pressure P in addition to lattice stress ik. Each of P and ik takes up a part of an external, or applied, pressure Pa (necessary for solid H4 e). The theory gives four pairs of propagating elastic modes, of which one corresponds to a fourth-sound mode, and a single diffusive mode, which has not been analyzed previously. The diffusive mode has three distinct velocities, with the superfluid velocity much larger than the normal fluid velocity, which in turn is much larger than the lattice velocity. The mode structure depends on the relative values of certain kinetic coefficients and thermodynamic derivatives. We consider pressurization experiments in solid H4 e at low temperatures in light of this diffusion mode and a previous analysis of modes in a normal solid with no superfluid component. 2010 The American Physical Society.