2 research outputs found
The vortex dynamics of a Ginzburg-Landau system under pinning effect
It is proved that the vortices are attracted by impurities or inhomogeities
in the superconducting materials. The strong H^1-convergence for the
corresponding Ginzburg-Landau system is also proved.Comment: 23page
Quantized vortex dynamics of the nonlinear Schr\"{o}dinger equation on torus with non-vanishing momentum
We derive rigorously the reduced dynamical laws for quantized vortex dynamics
of the nonlinear Schr\"{o}dinger equation on the torus with non-vanishing
momentum when the vortex core size {\epsilon} \to 0. The reduced dynamical laws
are governed by a Hamiltonian flow driven by a renormalized energy. A key
ingredient is to construct a new canonical harmonic map to include the effect
from the non-vanishing momentum into the dynamics. Finally, some properties of
the reduced dynamical law are discussed.Comment: 20 page