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09 February 2025
 
  » arxiv » 1109.0123

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Stochastic theory of quantum vortex on a sphere
Hiroshi Kuratsuji ;
Date 1 Sep 2011
AbstractA stochastic theory is presented for a quantum vortex that is expected to occur in superfluids coated on two dimensional sphere $ { m 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.
Source arXiv, 1109.0123
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