Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross–Pitaevskii Regime

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-19 DOI:10.1137/23m1608215

Christian Brennecke, Jinyeop Lee, Phan Thành Nam

引用次数: 0

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.

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吉布斯态还原密度矩阵在格罗斯-皮塔耶夫斯基机制中的二阶展开

SIAM 数学分析期刊》，第 56 卷第 4 期，第 5262-5284 页，2024 年 8 月。摘要。我们考虑了[math]中的[math]玻色子的平移不变系统，该系统通过在极限[math]中具有[math]阶散射长度的斥性双体势相互作用。我们推导了固定正温度下吉布斯态的单粒子和双粒子还原密度矩阵矩阵的二阶表达式，从而得到了波哥留波夫关于凝聚态周围波动的预言的合理性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

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.