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Phan Thanh, Nam; Salzmann, Robert (2020): Derivation of 3D Energy-Critical Nonlinear Schrodinger Equation and Bogoliubov Excitations for Bose Gases. In: Communications in Mathematical Physics, Vol. 375, No. 1: pp. 495-571
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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.