First order vortex dynamics
A non-dissipative vortex motion in a superconductor is considered. Using a Galilean invariant Lagrangian based on the Ginzburg-Landau model for time-dependent fields with kinetic terms linear in the first time derivatives of the fields, the author shows that for particular values of the coupling constants, the field dynamics reduces to first order differential equations for the vortex position. In this model, two vortices circle each other with constant speed and separation.
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