The 2D Chern-Simons-Schrödinger system reduced to 1D

2025/08/29 by Nicolas Rougerie, Rougerie, Nicolas, Qiyun Yang +1 · 1 citation
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.2508.21464

Abstract

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.

Citations

• Dimensional reduction for anyons in the average-field approximation
• Average-field approximation for very dilute almost-bosonic anyon gases
• Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons
• Existence and uniqueness of solutions to Liouville equation
• Derivation of the Chern-Simons-Schrödinger equation from the dynamics of an almost-bosonic-anyon gas
• A Lower-Dimensional Remnant of Flux Attachment
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• A generalized Liouville equation and magnetic stability
• Realization of a Laughlin state of two rapidly rotating fermions
• A Hydrodynamical Description of Bose Liquid with Fractional Exclusion Statistics
• Dimensional reduction for a system of 2D anyons
• Anyons in a tight wave-guide and the Tonks-Girardeau gas
• Vortex lattice solutions of the ZHK Chern-Simons equations
• Ground-state properties of anyons in a one-dimensional lattice
• The Average Field Approximation for Almost Bosonix Extended Anyons
• Stable NLS solitons in a cubic-quintic medium with a delta-function potential
• Elementary excitations of chiral Bose-Einstein condensates
• Local wellposedness of Chern-Simons-Schrödinger
• Dimensional Reduction of Two-Dimensional Anyons to a One-Dimensional Interacting Bose Gas
• Quasi-soliton and other behaviour of the nonlinear cubic-quintic Schrödinger equation

Cited by

• Dimensional reduction for anyons in the average-field approximation

Related

• Dimensional reduction for anyons in the average-field approximation
• Anyons in a tight wave-guide and the Tonks-Girardeau gas
• Abelian Chern-Simons field theory and anyon equation on a cylinder
• Dimensional reduction for a system of 2D anyons
• Microscopic derivation of the stationary Chern-Simons-Schrödinger equation for almost-bosonic anyons