Hydrodynamics of superfluids confined in blocked rings and wedges

Abstract

Motivated by many recent experimental studies of non-classical rotational inertia (NCRI) in superfluid and supersolid samples, we present a study of the hydrodynamics of a superfluid confined in the two-dimensional region (equivalent to a long cylinder) between two concentric arcs of radii $b$ and $a$ ($b<a$) subtending an angle $\beta$, with $0\le \beta \le 2\pi$. The case $\beta =2\pi$ corresponds to a blocked ring. We discuss the methodology to compute the NCRI effects, and calculate these effects both for small angular velocities, when no vortices are present, and in the presence of a vortex. We find that, for a blocked ring, the NCRI effect is small, and that therefore there will be a large discontinuity in the moment of inertia associated with blocking or unblocking circular paths. For blocked wedges ($b=0$) with $\beta >\pi$, we find an unexpected divergence of the velocity at the origin, which implies the presence of either a region of normal fluid or a vortex for {\it any} nonzero value of the angular velocity. Implications of our results for experiments on "supersolid" behavior in solid ${}^4\mathrm{He}$ are discussed. A number of mathematical issues are pointed out and resolved.

15 pages, including figures. To appear in Phys. Rev. E

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Cited by in corpus (3)

• Non-classical Rotational Inertia in a Two-dimensional Bosonic Solid Containing Grain Boundaries
• Dislocation Mobility and Anomalous Shear Modulus Effect in ${}^4$He Crystals
• Hydrodynamics of compressible superfluids in confined geometries