论连续体中相互作用费米子的热力学极限

arXiv - MATH - Operator Algebras Pub Date : 2024-09-16 DOI:arxiv-2409.10495

Oliver Siebert

{"title":"论连续体中相互作用费米子的热力学极限","authors":"Oliver Siebert","doi":"arxiv-2409.10495","DOIUrl":null,"url":null,"abstract":"We study the dynamics of non-relativistic fermions in $\\mathbb R^d$\ninteracting through a pair potential. Employing methods developed by Buchholz\nin the framework of resolvent algebras, we identify an extension of the CAR\nalgebra where the dynamics acts as a group of *-automorphisms, which are\ncontinuous in time in all sectors for fixed particle numbers. In addition, we\nidentify a suitable dense subalgebra where the time evolution is also strongly\ncontinuous. Finally, we briefly discuss how this framework could be used to\nconstruct KMS states in the future.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the thermodynamic limit of interacting fermions in the continuum\",\"authors\":\"Oliver Siebert\",\"doi\":\"arxiv-2409.10495\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the dynamics of non-relativistic fermions in $\\\\mathbb R^d$\\ninteracting through a pair potential. Employing methods developed by Buchholz\\nin the framework of resolvent algebras, we identify an extension of the CAR\\nalgebra where the dynamics acts as a group of *-automorphisms, which are\\ncontinuous in time in all sectors for fixed particle numbers. In addition, we\\nidentify a suitable dense subalgebra where the time evolution is also strongly\\ncontinuous. Finally, we briefly discuss how this framework could be used to\\nconstruct KMS states in the future.\",\"PeriodicalId\":501114,\"journal\":{\"name\":\"arXiv - MATH - Operator Algebras\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Operator Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.10495\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10495","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了$\mathbb R^d$中通过一对势相互作用的非相对论费米子的动力学。利用布霍尔茨（Buchholz）在解析代数框架内开发的方法，我们确定了CAR代数的一个扩展，在这个扩展中，动力学作为一个*-自变量组，对于固定粒子数，在所有扇区中都是时间连续的。此外，我们还确定了一个合适的稠密子代数，其中的时间演化也是强连续的。最后，我们简要讨论了未来如何利用这一框架来构建KMS状态。

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

On the thermodynamic limit of interacting fermions in the continuum

We study the dynamics of non-relativistic fermions in $\mathbb R^d$ interacting through a pair potential. Employing methods developed by Buchholz in the framework of resolvent algebras, we identify an extension of the CAR algebra where the dynamics acts as a group of *-automorphisms, which are continuous in time in all sectors for fixed particle numbers. In addition, we identify a suitable dense subalgebra where the time evolution is also strongly continuous. Finally, we briefly discuss how this framework could be used to construct KMS states in the future.

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

arXiv - MATH - Operator Algebras

自引率

0.00%

发文量