Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2023
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| author | Brennecke, Christian Lee, Jinyeop Nam, Phan Thành |
| author_facet | Brennecke, Christian Lee, Jinyeop Nam, Phan Thành |
| contents | We consider a translation-invariant system of $N$ bosons in $\mathbb{T}^{3}$ that interact through a repulsive two-body potential with scattering length of order $N^{-1}$ in the limit $N\to \infty$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_05448 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime Brennecke, Christian Lee, Jinyeop Nam, Phan Thành Mathematical Physics 81V70, 82B10 We consider a translation-invariant system of $N$ bosons in $\mathbb{T}^{3}$ that interact through a repulsive two-body potential with scattering length of order $N^{-1}$ in the limit $N\to \infty$. 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. |
| title | Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime |
| topic | Mathematical Physics 81V70, 82B10 |
| url | https://arxiv.org/abs/2310.05448 |