Andreev-Lifshitz Supersolid Hydrodynamics Including the Diffusive Mode

TL;DR

This paper re-examines the Andreev-Lifshitz supersolid hydrodynamics, revealing a previously unanalyzed diffusive mode with distinct velocities and exploring its implications for solid helium-4 under pressure.

Contribution

It introduces a detailed analysis of the diffusive mode in supersolid hydrodynamics, including its velocities and dependence on thermodynamic parameters.

Findings

Identifies a new diffusive mode with three distinct velocities.

Shows the superfluid velocity greatly exceeds the normal fluid and lattice velocities.

Provides insights into pressurization experiments in solid 4He at low temperatures.

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.