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

## TL;DR

This paper derives a 1D effective equation for a 2D anyon system with a Chern-Simons gauge field under strong anisotropic confinement, showing it reduces to a classical 1D quintic NLS equation.

## Contribution

The paper introduces a method to reduce a 2D Chern-Simons-Schrödinger system to a 1D equation using anisotropic trapping, providing a new link between anyon models and 1D nonlinear Schrödinger equations.

## Key findings

- Effective 1D dynamics governed by quintic NLS
- Reduction achieved through strong anisotropic trapping
- Provides a new approach for analyzing 2D anyon systems

## 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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Source: https://tomesphere.com/paper/2508.21464