The Lorentz Force Exerted by the Aharonov—Bohm Flux Line
Vortices in superfluids share certain similarities with the magnetic flux lines introduced to quantum mechanics by Aharonov and Bohm [1–3]. The Aharonov-Bohm (AB) line is a source of the vector potential A defined via the circulation ∳ dl • A = Φ, the same for any contour around the line. The magnetic field B = rot A is zero at every point except the line, and the total magnetic flux is fixed to Φ. The superfluid vortex circulation k is analogous to the magnetic flux Φ, and lines of the super-current around the vortex resembles the distribution of the vector potential A around the AB-line. Furthermore, the wave equation for a phonon scattered by a vortex  can be presented in a form identical to the Schrödinger equation for a charge in the field of the AB-line. Of course, the analogy should not be extended too far. Unlike the purely gauge vector potential, rot A — O, which can be chosen almost arbitrary due to the gauge invariance, the superflow is an observable field and the region around the vortex is not force-free. Nevertheless, the analogy has proven to be rather useful in the vortex theory, in particular, for the understanding of the origin of the Iordanskii force  (see also References ). One may say that the analog to the Iordanskii force is the transverse force exerted by the AB-line, which is a quantum version of the classical Lorentz force.
KeywordsVortex Coherence Mirror Symmetry Cond
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