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arXiv · 2508.21464

The 2D Chern-Simons-Schr{\"o}dinger system reduced to 1D

Nicolas Rougerie·Qiyun Yang
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Abstract

We study a mean-field model for a system of 2D abelian anyons, given by the dynamics of a Schr{\"o}dinger 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 Schr{\"o}dinger 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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Nicolas Rougerie, Qiyun Yang. 2025-08-29. The 2D Chern-Simons-Schr{\"o}dinger system reduced to 1D. https://arxiv.org/abs/2508.21464

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