不可区分量子粒子的熵关系

IF 2.2 3区 物理与天体物理 Q2 MECHANICS
Marius Lemm
{"title":"不可区分量子粒子的熵关系","authors":"Marius Lemm","doi":"10.1088/1742-5468/ad343a","DOIUrl":null,"url":null,"abstract":"The von Neumann entropy of a <italic toggle=\"yes\">k</italic>-body-reduced density matrix <italic toggle=\"yes\">γ</italic>\n<sub>\n<italic toggle=\"yes\">k</italic>\n</sub> quantifies the entanglement between <italic toggle=\"yes\">k</italic> quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of <italic toggle=\"yes\">k</italic>; it is concave for all <inline-formula>\n<tex-math><?CDATA $1\\unicode{x2A7D} k\\unicode{x2A7D} N$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mtext>⩽</mml:mtext><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mi>N</mml:mi></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"jstatad343aieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> and non-decreasing until the midpoint <inline-formula>\n<tex-math><?CDATA $k\\unicode{x2A7D} \\lfloor{N/2} \\rfloor$?></tex-math>\n<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mo fence=\"false\" stretchy=\"false\">⌊</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">⌋</mml:mo></mml:mrow></mml:math>\n<inline-graphic xlink:href=\"jstatad343aieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula>. The results hold for indistinguishable quantum particles and are independent of the statistics.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Entropic relations for indistinguishable quantum particles\",\"authors\":\"Marius Lemm\",\"doi\":\"10.1088/1742-5468/ad343a\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The von Neumann entropy of a <italic toggle=\\\"yes\\\">k</italic>-body-reduced density matrix <italic toggle=\\\"yes\\\">γ</italic>\\n<sub>\\n<italic toggle=\\\"yes\\\">k</italic>\\n</sub> quantifies the entanglement between <italic toggle=\\\"yes\\\">k</italic> quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of <italic toggle=\\\"yes\\\">k</italic>; it is concave for all <inline-formula>\\n<tex-math><?CDATA $1\\\\unicode{x2A7D} k\\\\unicode{x2A7D} N$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mn>1</mml:mn><mml:mtext>⩽</mml:mtext><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mi>N</mml:mi></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"jstatad343aieqn1.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> and non-decreasing until the midpoint <inline-formula>\\n<tex-math><?CDATA $k\\\\unicode{x2A7D} \\\\lfloor{N/2} \\\\rfloor$?></tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:mrow><mml:mi>k</mml:mi><mml:mtext>⩽</mml:mtext><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⌊</mml:mo><mml:mrow><mml:mi>N</mml:mi><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mo fence=\\\"false\\\" stretchy=\\\"false\\\">⌋</mml:mo></mml:mrow></mml:math>\\n<inline-graphic xlink:href=\\\"jstatad343aieqn2.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula>. The results hold for indistinguishable quantum particles and are independent of the statistics.\",\"PeriodicalId\":17207,\"journal\":{\"name\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Statistical Mechanics: Theory and Experiment\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1742-5468/ad343a\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Statistical Mechanics: Theory and Experiment","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1742-5468/ad343a","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 0

摘要

一个 k 体还原密度矩阵 γk 的冯-诺依曼熵量化了 k 个量子粒子与其余粒子之间的纠缠。在本文中,我们严格证明了这种纠缠熵作为 k 的函数的一般性质;它对所有 1⩽k⩽N 都是凹的,并且在中点 k⩽⌊N/2⌋ 之前是不递减的。这些结果适用于不可区分的量子粒子,并且与统计量无关。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Entropic relations for indistinguishable quantum particles
The von Neumann entropy of a k-body-reduced density matrix γ k quantifies the entanglement between k quantum particles and the remaining ones. In this paper, we rigorously prove general properties of this entanglement entropy as a function of k; it is concave for all 1kN and non-decreasing until the midpoint kN/2 . The results hold for indistinguishable quantum particles and are independent of the statistics.
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
CiteScore
4.50
自引率
12.50%
发文量
210
审稿时长
1.0 months
期刊介绍: JSTAT is targeted to a broad community interested in different aspects of statistical physics, which are roughly defined by the fields represented in the conferences called ''Statistical Physics''. Submissions from experimentalists working on all the topics which have some ''connection to statistical physics are also strongly encouraged. The journal covers different topics which correspond to the following keyword sections. 1. Quantum statistical physics, condensed matter, integrable systems Scientific Directors: Eduardo Fradkin and Giuseppe Mussardo 2. Classical statistical mechanics, equilibrium and non-equilibrium Scientific Directors: David Mukamel, Matteo Marsili and Giuseppe Mussardo 3. Disordered systems, classical and quantum Scientific Directors: Eduardo Fradkin and Riccardo Zecchina 4. Interdisciplinary statistical mechanics Scientific Directors: Matteo Marsili and Riccardo Zecchina 5. Biological modelling and information Scientific Directors: Matteo Marsili, William Bialek and Riccardo Zecchina
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信