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arXiv · 2310.05448

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

Christian Brennecke·Jinyeop Lee·Phan Thành Nam
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Abstract

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.

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Christian Brennecke, Jinyeop Lee, Phan Thành Nam. 2023-10-09. Second Order Expansion of Gibbs State Reduced Density Matrices in the Gross-Pitaevskii Regime. https://doi.org/10.1137/23m1608215

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