{"title":"二维任子体系的降维","authors":"Nicolas Rougerie, Qiyun Yang","doi":"10.1007/s00023-024-01417-2","DOIUrl":null,"url":null,"abstract":"<div><p>Anyons with a statistical phase parameter <span>\\(\\alpha \\in (0,2)\\)</span> 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 <i>y</i>-direction than in the <i>x</i>-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 <i>x</i>-direction is given by the impenetrable Tonks–Girardeau Bose gas, which has no dependency on <span>\\(\\alpha \\)</span>, and no trace left of the long-range interactions of the 2D model.\n</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"25 11","pages":"4987 - 5018"},"PeriodicalIF":1.4000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Dimensional reduction for a system of 2D anyons\",\"authors\":\"Nicolas Rougerie, Qiyun Yang\",\"doi\":\"10.1007/s00023-024-01417-2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Anyons with a statistical phase parameter <span>\\\\(\\\\alpha \\\\in (0,2)\\\\)</span> 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 <i>y</i>-direction than in the <i>x</i>-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 <i>x</i>-direction is given by the impenetrable Tonks–Girardeau Bose gas, which has no dependency on <span>\\\\(\\\\alpha \\\\)</span>, and no trace left of the long-range interactions of the 2D model.\\n</p></div>\",\"PeriodicalId\":463,\"journal\":{\"name\":\"Annales Henri Poincaré\",\"volume\":\"25 11\",\"pages\":\"4987 - 5018\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-02-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Poincaré\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00023-024-01417-2\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales Henri Poincaré","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s00023-024-01417-2","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
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.我们考虑的是紧密波导中任子的二维系统的降维问题。更具体地说,我们研究了二维磁规图像模型,该模型具有强加的各向异性谐波势,它在 y 方向上对粒子的捕获比在 x 方向上强得多。我们证明,在这种还原过程中,特征能和特征函数都渐近地解耦为松约束方向和紧约束方向。x方向的极限一维系统是由不可穿透的唐克斯-吉拉尔多玻色气体给出的,它与\(\alpha \)无关,也没有二维模型长程相互作用的痕迹。
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.
期刊介绍:
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.