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arXiv · 1109.0123

Stochastic theory of quantum vortex on a sphere

Hiroshi Kuratsuji
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Abstract

A stochastic theory is presented for a quantum vortex that is expected to occur in superfluids coated on two dimensional sphere $ {\rm S}^2 $. The starting point is the canonical equation of motion (the Kirchhoff equation) for a point vortex, which is derived using the time-dependent Landau-Ginzburg theory. The vortex equation, which is equivalent to the spin equation, turns out to be the Langevin equation, from which the Fokker-Planck equation is obtained by using the functional integral technique. The Fokker-Planck equation is solved for several typical cases of the vortex motion by noting the specific form of pinning potential. An extension to the non-spherical vortices is briefly discussed for the case of the vortex on plane and pseudo-sphere.

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Hiroshi Kuratsuji. 2011-09-01. Stochastic theory of quantum vortex on a sphere. https://doi.org/10.1103/physreve.85.031150

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