Andreev-Lifshitz Supersolid Hydrodynamics Including the Diffusive Mode

Abstract

We have re-examined 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 ${\lambda }_{ik}$. Each of $P$ and ${\lambda }_{ik}$ takes up a part of an external, or applied, pressure $P_a$ (necessary for solid 4He). The theory gives four pairs of propagating elastic modes, of which one pair 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 4He at low temperatures in light of this diffusion mode and a previous analysis of modes in a normal solid with no superfluid component.

8 pages. Accepted by Physical Review B

References in corpus (11)

• Low Temperature Shear Modulus Changes in Solid 4-He and Connection to Supersolidity
• Disorder and the Supersolid State of Solid ${}^4$He
• Oscillation Frequency Dependence of Non-Classical Rotation Inertia of Solid ${}^4$He
• Evidence for a Superglass State in Solid 4He
• Observation of non-classical rotational inertia in bulk solid 4He
• Annealing Effect for Supersolid Fraction in ${}^4$He
• Nonclassical Rotational Inertia in Single Crystal Helium
• Probing the Upper Limit of Nonclassical Rotational Inertia
• Bounds for the Superfluid Fraction from Exact Quantum Monte Carlo Local Densities
• Andreev-Lifshitz Hydrodynamics Applied to an Ordinary Solid under Pressure
• Generation Efficiencies for Propagating Modes in a Supersolid

Cited by in corpus (2)

• Universality Classes of Relativistic Fluid Dynamics: Foundations
• Universality Classes of Relativistic Fluid Dynamics: Applications