{"title":"Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross–Pitaevskii Regime","authors":"Christian Brennecke, Jinyeop Lee, Phan Thành Nam","doi":"10.1137/23m1608215","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5262-5284, August 2024. <br/> Abstract. We consider a translation-invariant system of [math] bosons in [math] that interact through a repulsive two-body potential with scattering length of order [math] in the limit [math]. We derive second order expressions for the one- and two-particle reduced density matrix matrices of the Gibbs state at fixed positive temperatures, thus obtaining a justification of Bogoliubov’s prediction on the fluctuations around the condensate.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1608215","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 5262-5284, August 2024. Abstract. We consider a translation-invariant system of [math] bosons in [math] that interact through a repulsive two-body potential with scattering length of order [math] in the limit [math]. We derive second order expressions for the one- and two-particle reduced density matrix matrices of the Gibbs state at fixed positive temperatures, thus obtaining a justification of Bogoliubov’s prediction on the fluctuations around the condensate.
期刊介绍：
SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena.
Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere.
Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.
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