1D quasi-solutions of the 2D Chern-Simons-Schrödinger system
Résumé
We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schrödinger matter field coupled to a Chern-Simons gauge field. We derive an effective 1D equation by adding a strongly anisotropic trapping potential (wave-guide) acting on the Schrödinger field, and tracing out the tight confinement direction. The effective dynamics in the loose direction of the wave-guide turns out to be governed by the classical 1D quintic NLS equation.
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