玻色吉布斯态的动力学经典场极限：二维和三维中的重整化哈特雷斯非线性薛定谔方程关联
Dynamical classical-field limit of Bosonic Gibbs states: Renormalized Hartree NLS correlations in 2D and 3D
AI总结：
该研究推导了二维和三维环面上重整化哈特雷斯非线性薛定谔方程的时变关联函数，其证明结合了量子生成元收敛性与刘维尔方程正解唯一性，填补了高维玻色吉布斯态经典场极限研究的空白。
AI中文摘要：
本文从对应的玻色多体吉布斯动力学出发，推导了二维和三维环面$\boldsymbol{\top^d}$上重整化哈特雷斯非线性薛定谔方程的时变关联函数。与Fröhlich、Knowles、Schlein和Sohinger此前研究的一维问题不同，高维中缩放后的量子粒子数并非一致有界，相关经典场需要Wick重整化。我们的证明结合了加权希尔伯特空间中量子生成元的收敛性，以及受吉布斯测度支配的极限刘维尔方程正解的唯一性。
英文摘要：
In this paper we derive the time-dependent correlation functions of the renormalized Hartree NLS equation on the torus $\mathbb T^d$, $d=2,3$, from the corresponding bosonic many-body Gibbs dynamics. In contrast with the 1D problem studied earlier by Fröhlich, Knowles, Schlein and Sohinger, in higher dimensions the scaled quantum particle number is not uniformly bounded and the relevant classical fields require Wick renormalization. Our proof combines convergence of the quantum generators in weighted Hilbert spaces with uniqueness for positive solutions of the limiting Liouville equation that are dominated by the Gibbs measure.
