SECOND ORDER EXPANSION OF GIBBS STATE REDUCED DENSITY MATRICES IN THE GROSS-PITAEVSKII REGIME

Christian Brennecke; Jinyeop Lee; Phan Thanh Nam

doi:10.1137/23M1608215

SECOND ORDER EXPANSION OF GIBBS STATE REDUCED DENSITY MATRICES IN THE GROSS-PITAEVSKII REGIME

Christian Brennecke
, Jinyeop Lee
, Phan Thanh Nam

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider a translation-invariant system of N bosons in \BbbT³ that interact through a repulsive two-body potential with scattering length of order N^-¹ in the limit N \rightarrow \infty. 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.

Original language	English
Pages (from-to)	5262-5284
Number of pages	23
Journal	SIAM Journal on Mathematical Analysis
Volume	56
Issue number	4
DOIs	https://doi.org/10.1137/23M1608215
Publication status	Published - Aug 2024

Bibliographical note

Publisher Copyright:
Copyright © 2024 by SIAM.

Keywords

Bogoliubov transformation
Bose-Einstein condensation
Gibbs state
Gross-Pitaevskii regime
reduced densities

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10.1137/23M1608215

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title = "SECOND ORDER EXPANSION OF GIBBS STATE REDUCED DENSITY MATRICES IN THE GROSS-PITAEVSKII REGIME",

abstract = "We consider a translation-invariant system of N bosons in \textbackslash{}BbbT3 that interact through a repulsive two-body potential with scattering length of order N-1 in the limit N \textbackslash{}rightarrow \textbackslash{}infty. 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.",

keywords = "Bogoliubov transformation, Bose-Einstein condensation, Gibbs state, Gross-Pitaevskii regime, reduced densities",

author = "Christian Brennecke and Jinyeop Lee and Nam, \{Phan Thanh\}",

note = "Publisher Copyright: Copyright {\textcopyright} 2024 by SIAM.",

year = "2024",

month = aug,

doi = "10.1137/23M1608215",

language = "English",

volume = "56",

pages = "5262--5284",

journal = "SIAM Journal on Mathematical Analysis",

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AU - Brennecke, Christian

AU - Lee, Jinyeop

AU - Nam, Phan Thanh

PY - 2024/8

Y1 - 2024/8

N2 - We consider a translation-invariant system of N bosons in \BbbT3 that interact through a repulsive two-body potential with scattering length of order N-1 in the limit N \rightarrow \infty. 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.

AB - We consider a translation-invariant system of N bosons in \BbbT3 that interact through a repulsive two-body potential with scattering length of order N-1 in the limit N \rightarrow \infty. 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.

KW - Bogoliubov transformation

KW - Bose-Einstein condensation

KW - Gibbs state

KW - Gross-Pitaevskii regime

KW - reduced densities

UR - https://www.scopus.com/pages/publications/85199497193

U2 - 10.1137/23M1608215

DO - 10.1137/23M1608215

M3 - Article

AN - SCOPUS:85199497193

SN - 0036-1410

VL - 56

SP - 5262

EP - 5284

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 4

ER -

SECOND ORDER EXPANSION OF GIBBS STATE REDUCED DENSITY MATRICES IN THE GROSS-PITAEVSKII REGIME

Abstract

Bibliographical note

Keywords

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