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• W2013102775 abstract "We study a nonlinear system of partial differential equations in which a complex field (the Higgs field) evolves according to a nonlinear Schrödinger equation, coupled to an electromagnetic field whose time evolution is determined by a Chern-Simons term in the action. In two space dimensions, the Chern-Simons dynamics is a Galileo invariant evolution for A, which is an interesting alternative to the Lorentz invariant Maxwell evolution, and is finding increasing numbers of applications in two dimensional condensed matter field theory. The system we study, introduced by Manton, is a special case (for constant external magnetic field, and a point interaction) of the effective field theory of Zhang, Hansson and Kivelson arising in studies of the fractional quantum Hall effect. From the mathematical perspective the system is a natural gauge invariant generalization of the nonlinear Schrödinger equation, which is also Galileo invariant and admits a self-dual structure with a resulting large space of topological solitons (the moduli space of self-dual Ginzburg-Landau vortices). We prove a theorem describing the adiabatic approximation of this system by a Hamiltonian system on the moduli space. The approximation holds for values of the Higgs self-coupling constant λ close to the self-dual (Bogomolny) value of 1. The viability of the approximation scheme depends upon the fact that self-dual vortices form a symplectic submanifold of the phase space (modulo gauge invariance). The theorem provides a rigorous description of slow vortex dynamics in the near self-dual limit." @default.
• W2013102775 created "2016-06-24" @default.
• W2013102775 creator A5004491301 @default.
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• W2013102775 date "2009-06-18" @default.
• W2013102775 modified "2023-09-25" @default.
• W2013102775 title "Adiabatic Limit and the Slow Motion of Vortices in a Chern-Simons-Schrödinger System" @default.
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• W2013102775 doi "https://doi.org/10.1007/s00220-009-0844-y" @default.
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