Two-dimensional superflow past an obstacle of arbitrary penetrability: Exact results for the critical velocity
Résumé
We present theoretical results concerning the critical velocity for dissipationless motion of a two-dimensional nonlinear Schrödinger superfluid past a static obstacle represented by a repulsive potential of large width. In contrast to most of the state of the art, our study is not restricted to an impenetrable obstacle potential nor to a quartic interaction Hamiltonian, which makes it possible to get closer to recent experiments with atomic Bose-Einstein condensates and paraxial superfluids of light. Our analytical approach of the equations modeling the hydrodynamics of the superfluid relies on an analogue of the hydraulic approximation, the hodograph method, and Janzen-Rayleigh expansions of the velocity potential. A very good agreement with imaginary-time numerical calculations is shown.
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