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We derive the asymptotical dynamical law for Ginzburg-Landau vortices in the plane under the Schrödinger dynamics, as the Ginzburg-Landau parameter goes to zero. The limiting law is the wellknown point-vortex system. This result extends to the whole plane previous results of [8, 13] established for bounded domains, and holds for arbitrary degree at infinity. When this degree is non-zero, the total Ginzburg-Landau energy is infinite.

On the NLS dynamics for infinite energy vortex configurations on the plane