Derivation of 3D Energy-Critical Nonlinear Schrödinger Equation and Bogoliubov Excitations for Bose Gases
Derivation of 3D Energy-Critical Nonlinear Schrödinger Equation and Bogoliubov Excitations for Bose Gases
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DOI：
10.1007/s00220-019-03480-x
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发表时间：
2018-10
影响因子：
2.4
通讯作者：
P. T. Nam;Robert Salzmann
中科院分区：
文献类型：
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作者：
P. T. Nam;Robert Salzmann
我们导出了三体相互作用玻色气体的平均场极限的三维五次NLS。五次NLS是能量关键的，与从玻色气体中产生的具有对相互作用的立方NLS相比，导致了一些新的困难。我们的方法是基于Bogoliubov的近似，它也提供了关于凝聚体周围的涨落的信息，以当时的体波函数的范数近似的形式。
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 theN-body wave function.