arXiv subjects

Qiyun Yang

Publications and source records attributed to Qiyun Yang.

4 recordsLinked to original sources

arXiv2025

Dimensional reduction for anyons in the average-field approximation

We study abelian anyons at the mean-field/almost-bosonic level, whose dynamics are governed by the Chern-Simons-Schr\"odinger system. We consider the dimensional reduction of this 2D model by introducing an anisotropic trapping potential, and derive an effective 1D model after tracing out the tight confinement direction. The resulting effective dynamics in the loose confinement direction is captured by a quintic defocusing nonlinear Schr\"odinger equation. We rigorously establish this dimensional reduction process in the sense of ground state energies and time-dependent solutions, under an $H^2$ well-posedness assumption.

math.AP↗

arXiv2025

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

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.

math.AP↗

arXiv2024

Dimensional reduction for a system of 2D anyons

Anyons with a statistical phase parameter $α\in(0,2)$ are a kind of quasi-particles that, for topological reasons, only exist in a 1D or 2D world. We consider the dimensional reduction for a 2D system of anyons in a tight wave-guide. More specifically, we study the 2D magnetic-gauge picture model with an imposed anisotropic harmonic potential that traps particles much stronger in the $y$-direction than in the $x$-direction. We prove that both the eigenenergies and the eigenfunctions are asymptotically decoupled into the loose confining direction and the tight confining direction during this reduction. The limit 1D system for the $x$-direction is given by the impenetrable Tonks-Girardeau Bose gas, which has no dependency on $α$, and no trace left of the long-range interactions of the 2D model.

math.AP↗

arXiv2023

Anyons in a tight wave-guide and the Tonks-Girardeau gas

We consider a many-body system of 2D anyons, free quantum particles with general statistics parameter α\in ]0,2[. In the magnetic gauge picture they are described as bosons attached to Aharonov-Bohm fluxes of intensity 2 παgenerating long-range magnetic forces. A dimensional reduction to 1D is obtained by imposing a strongly anisotropic trapping potential. This freezes the motion in the direction of strong trapping, leading to 1D physics along the weak direction. The latter is governed to leading order by the Tonks-Girardeau model of impenetrable bosons, independently of α.

math.AP↗