Slow Schrödinger dynamics of gauged vortices
Abstract
Multivortex dynamics in Manton's SchrödingerChernSimons variant of the LandauGinzburg model of thin superconductors is studied within a moduli space approximation. It is shown that the reduced flow on {\sf M}_N , the Nvortex moduli space, is Hamiltonian with respect to \omega_{L^2} , the L^{2} Kähler form on {\sf 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 ({\sf 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 3vortex 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.
 Publication:

Nonlinearity
 Pub Date:
 July 2004
 DOI:
 10.1088/09517715/17/4/010
 arXiv:
 arXiv:hepth/0403215
 Bibcode:
 2004Nonli..17.1337R
 Keywords:

 High Energy Physics  Theory
 EPrint:
 22 pages, 2 figures