We derive the 3D quintic NLS as the mean field limit of a Bose gas with three-body interactions. The quintic NLS is energy-critical, leading to several new difficulties in comparison with the cubic NLS which emerges from Bose gases with pair-interactions. Our method is based on Bogoliubov’s approximation, which also provides the information on the fluctuations around the condensate in terms of a norm approximation for the N -body wave function.

中文翻译：

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玻色气体的 3D 能量临界非线性薛定谔方程和 Bogoliubov 激发的推导

我们将 3D 五次 NLS 推导出为具有三体相互作用的 Bose 气体的平均场极限。五次 NLS 对能量至关重要，与从具有配对相互作用的 Bose 气体中产生的三次 NLS 相比，导致了几个新的困难。我们的方法基于 Bogoliubov 近似，它也根据 N 体波函数的范数近似提供了关于凝聚物周围波动的信息。