Vortex Pair Energy in an Anisotropic Superfluid Film

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The energy and impulse of a vortex pair are calculated for a helium film in which the superfluid density is anisotropic in the plane of the film, such as might be induced by a supercurrent. Surprisingly, the energy of the pair in its rest frame is found not to depend on the angle between the anisotropy direction and the axis of the pair, but to have the same form as for an isotropic film, the only change being that the superfluid density is replaced by the geometric mean of the parallel and perpendicular components of the superfluid tensor.

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