{
  "id": "2305.06670",
  "version": "v1",
  "published": "2023-05-11T09:10:21.000Z",
  "updated": "2023-05-11T09:10:21.000Z",
  "title": "Dimensional reduction for a system of 2D anyons",
  "authors": [
    "Nicolas Rougerie",
    "Qiyun Yang"
  ],
  "categories": [
    "math.AP",
    "cond-mat.quant-gas",
    "math-ph",
    "math.MP",
    "math.SP",
    "quant-ph"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-11T09:10:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimensional reduction",
      "2d anyons",
      "2d magnetic-gauge picture model",
      "confining direction",
      "imposed anisotropic harmonic potential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}