2004/03/22 by Nuno M. Romão, N. M. Romao, Martin Speight +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Euclidean geometry #Euclidean space #Geometry #Hamiltonian (control theory) #Hamiltonian mechanics #Hamiltonian system #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Moduli space #Phase space #Physics #Physics of Superconductivity and Magnetism #Quantum mechanics #Quantum, superfluid, helium dynamics #Vortex #hep-th
paper · pdf · doi:10.1088/0951-7715/17/4/010
published as Nonlinearity.17:1337-1355,2004 · 22 pages, 2 figures
arxiv created 2004/03/22 · openalex publication_date 2004/04/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 L 2 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.