弱相互作用玻色气体基态的大偏差

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-07-02 DOI:10.1007/s00023-024-01463-w

Simone Rademacher

{"title":"弱相互作用玻色气体基态的大偏差","authors":"Simone Rademacher","doi":"10.1007/s00023-024-01463-w","DOIUrl":null,"url":null,"abstract":"<div><p>We consider the ground state of a Bose gas of <i>N</i> particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit <span>\\(N \\rightarrow \\infty \\)</span> bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.</p></div>","PeriodicalId":463,"journal":{"name":"Annales Henri Poincaré","volume":"26 4","pages":"1239 - 1289"},"PeriodicalIF":1.4000,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00023-024-01463-w.pdf","citationCount":"0","resultStr":"{\"title\":\"Large Deviations for the Ground State of Weakly Interacting Bose Gases\",\"authors\":\"Simone Rademacher\",\"doi\":\"10.1007/s00023-024-01463-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We consider the ground state of a Bose gas of <i>N</i> particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit <span>\\\\(N \\\\rightarrow \\\\infty \\\\)</span> bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.</p></div>\",\"PeriodicalId\":463,\"journal\":{\"name\":\"Annales Henri Poincaré\",\"volume\":\"26 4\",\"pages\":\"1239 - 1289\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2024-07-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00023-024-01463-w.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales Henri Poincaré\",\"FirstCategoryId\":\"4\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00023-024-01463-w\",\"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/s00023-024-01463-w","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

我们考虑了三维单位环上由 N 个粒子组成的玻色气体的基态，该玻色气体在均场机制下表现出玻色-爱因斯坦凝聚。通过相互作用的玻色气体基态给出的有界一粒子算子定律对应于玻色子相关性引起的依存随机变量。我们证明，在极限（N \rightarrow \infty \）下，通过基态给出规律的有界单粒子算子满足大偏差估计。我们推导出了速率函数的下限和上限，它们匹配到二阶，并以凝聚态周围的量子波动为特征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Large Deviations for the Ground State of Weakly Interacting Bose Gases

We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose–Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables due to the bosons’ correlation. We prove that in the limit \(N \rightarrow \infty \) bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

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.