University of Minnesota
School of Physics & Astronomy


Hydrodynamics of Superfluids Confined in Blocked Rings and Wedges


by Chandan Dasgupta and Oriol T. Valls in Phys. Rev. E79, 016303 (2009).

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 β , with 0≤β≤2π . The case β = 2π 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 β > π , 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{\rm He} are discussed. A number of mathematical issues are pointed out and resolved.

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