On the Superfluid Fraction and the Hydrodynamics of Supersolids
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This review largely considers the author's extensions of two foundation works in supersolids: Andreev and Lifshitz's hydrodynamics, and Leggett's Non- Classical Rotational Inertia (NCRI) with estimates of the T = 0 upper limit. Relative to the case of a perfect lattice, the Andreev and Lifshitz equations contain an additional degree of freedom, which permits a liquid-like internal pressure P that is distinct from the lattice stress (or 'solid-like pressure'). This is particularly relevant to 4He, which requires an applied pressure P a to solidify; use of a Maxwell relation relating P and strain yields that P P a2; we estimate that near the melting pressure the liquid-like pressure in equilibrium is about 1/4 of the solid-like pressure. This new freedom also permits vacancy diffusion, which we have studied for both ordinary solids and supersolids. In both cases, for the vacancy diffusion mode the liquid-like pressure and the lattice stress cancel. Further, since at T = 0 the supersolid fraction f s is less than unity and the excitation part of the normal fraction is zero, we argue that there must be an additional source of "normal" mass, to which we attribute a velocity that in principle is distinct from the lattice velocity associated with elasticity. Relative to NCRI we have made numerous estimates of the upper limit for the superfluid fraction f s; we find f s values on the order of 0.2 for realistic models of the atomic density. Correlation effects in the solid cause the superfluid velocity v s of one particle to depend on correlations with the positions of other particles, and this leads to a more complex theory for the flow pattern and for the upper limit on f s. Springer Science+Business Media, LLC 2012.
