Current-Phase Relation for Flow of an S-Wave Paired Superfluid through a Cylindrical Channel of Finite Length

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Abstract
The Ginzburg-Landau equations are used to investigate superflow through a cylindrical orifice of radius R and length L. The order parameter is taken to be a complex scalar ψ, appropriate to an s-wave paired superfluid. It is assumed that ψ=0 on the surfaces of the orifice and that rigid boundary conditions may be employed at the ends of the tube. The use of a variational form for the radial variation of ψ reduces the problem to a one dimensional one. The critical value of L for each value of R has been calculated at which changeover from a single-valued to a multivalued current-phase relation occurs. The maximum supercurrent for tubes of various geometries has also been calculated.

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