Dimensional reduction for a system of 2D anyons

• URL: http://arxiv.org/abs/2305.06670v2
• Date: Fri, 29 Mar 2024 10:07:15 GMT
• Title: Dimensional reduction for a system of 2D anyons
• Authors: Nicolas Rougerie, Qiyun Yang,
• Abstract summary: We consider the dimensional reduction for a 2D system of anyons in a tight wave-guide. We prove that both the eigenenergies and the eigenfunctions are decoupled into the loose confining direction and the tight confining direction during this reduction. The limit 1D for the $x$-direction is given by the impenetrable Tonks-Girardeau Bose gas, which has no dependency on $alpha$, and no trace left of the long-range interactions of the 2D model.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Anyons with a statistical phase parameter $\alpha\in(0,2)$ 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 $\alpha$, and no trace left of the long-range interactions of the 2D model.

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