The 2D Chern-Simons-Schr{\"o}dinger system reduced to 1D
Analysis of PDEs
2026-01-27 v2 Mesoscale and Nanoscale Physics
Quantum Gases
Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2508.21464,
title = {The 2D Chern-Simons-Schr{\"o}dinger system reduced to 1D},
author = {Nicolas Rougerie and Qiyun Yang},
journal= {arXiv preprint arXiv:2508.21464},
year = {2026}
}