带有调和势的Anderson-Hartree方程的一种简单推导
A simple derivation of Anderson-Hartree equations with harmonic potential
AI总结：
本文适配Hartree方程的推导，针对含Anderson-Hermite算子的情况，通过能量估计实现平均场极限与噪声极限的交换。
AI中文摘要：
本文展示了如何对Knowles和Pickl提出的Hartree方程推导进行适配，适用于单粒子哈密顿量为1维和2维的Anderson-Hermite算子，或3维的形式Anderson-Hermite算子的情况。通过对极限方程解证明有界集合中噪声一致的能量估计，我们实现了双重极限，即证明可将平均场极限与噪声极限交换。
英文摘要：
In this paper, we show how to adapt a derivation of Hartree equations due to Knowles and Pickl in the case where the one-particle hamiltonian is an Anderson-Hermite operator in dimension 1 and 2 or a formal Anderson-Hermite operator in dimension 3. By proving energy estimates for solution of the limit equation, uniform in the noise in bounded sets, we achieve a double limit. Namely, we show that we can commute the mean-field limit with a limit in noise.
