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 M N , the N vortex moduli space, is hamiltonian with respect to ω L 2 , the L 2 Kähler 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 , ω L 2) is not hamiltonian. It is argued that the N = 3 flow is integrable in the sense of Liouville. Asymptotic formulae for ω 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.