Slow Schroedinger dynamics of gauged vortices

Details Slow Schroedinger dynamics of gauged vortices Slow Schroedinger dynamics of gauged vortices

2004-03-22

arxiv.org/abs/hep-th/0403215v1

Nonlinearity.17:1337-1355,2004

Physics

High Energy Physics

High Energy Physics - Theory

22 pages, 2 figures

Scientific paper

10.1088/0951-7715/17/4/010

Multivortex dynamics in Manton's Schroedinger--Chern--Simons variant of the Landau-Ginzburg model of thin superconductors is studied within a moduli space approximation. It is shown that the reduced flow on M_N, the N vortex moduli space, is hamiltonian with respect to \omega_{L^2}, the L^2 Kaehler form on \M_N. A purely hamiltonian discussion of the conserved momenta associated with the euclidean symmetry of the model is given, and it is shown that the euclidean action on (M_N,\omega_{L^2}) is not hamiltonian. It is argued that the N=3 flow is integrable in the sense of Liouville. Asymptotic formulae for \omega_{L^2} and the reduced Hamiltonian for large intervortex separation are conjectured. Using these, a qualitative analysis of internal 3-vortex dynamics is given and a spectral stability analysis of certain rotating vortex polygons is performed. Comparison is made with the dynamics of classical fluid point vortices and geostrophic vortices.

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