In this paper, we investigate the quantum many-body dynamics with a linear combination of many-body interactions. We derive rigorously the nonlinear Schrödinger equation with a general nonlinearity as the mean-field limit of this model. Due to the complex interaction structure, we establish a new energy estimate for $0<\beta <\frac{1}{(m-1)d}$, which is efficient to handle the case of many-body interactions and allows us to obtain the mean-field approximation on longer length scales than the previous result in the work of Xie [Differ. Integr. Equations 28, 455–504 (2015)].

中文翻译：

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一维和二维具有一般非线性和Gross-Pitaevskii层次结构的非线性Schrödinger方程的推导

在本文中，我们研究了多体相互作用的线性组合的量子多体动力学。我们严格推导非线性Schrödinger方程，该方程具有一般非线性作为该模型的平均场极限。由于复杂的相互作用结构，我们为$0<\beta <\frac{\mathrm{1个}}{（米-\mathrm{1个}）d}$，它可以有效地处理多体相互作用的情况，并且使我们能够在比Xie [Differ。整数 方程28，455-504（2015）]。