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Pré-Publication, Document De Travail Année : 2023

Dimensional reduction for a system of 2D anyons

Résumé

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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Dates et versions

hal-04094099 , version 1 (10-05-2023)
hal-04094099 , version 2 (08-12-2023)

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Nicolas Rougerie, Qiyun Yang. Dimensional reduction for a system of 2D anyons. 2023. ⟨hal-04094099v1⟩
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