Slow Schrödinger dynamics of gauged vortices

Multivortex dynamics in Manton's Schrödinger–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 , the N-vortex moduli space, is Hamiltonian with respect to , the L2 Kähler form on . 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 is not Hamiltonian. It is argued that the N = 3 flow is integrable in the sense of Liouville. Asymptotic formulae for 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.