Stochastic theory of quantum vortex on a sphere
Statistical Mechanics
2015-05-30 v1 Mesoscale and Nanoscale Physics
Quantum Physics
Abstract
A stochastic theory is presented for a quantum vortex that is expected to occur in superfluids coated on two dimensional sphere . 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.
Cite
@article{arxiv.1109.0123,
title = {Stochastic theory of quantum vortex on a sphere},
author = {Hiroshi Kuratsuji},
journal= {arXiv preprint arXiv:1109.0123},
year = {2015}
}