School of Physics & Astronomy

# Hydrodynamics of Superfluids confined to blocked rings and wedges

by C. Dasgupta and Oriol T. Valls in Phys. Rev. E 79, 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 He-4 are discussed. A number of mathematical issues are pointed out and resolved.

More information at http://link.aps.org/doi/10.1103/PhysRevE.79.016303