Derivation of 3D Energy-Critical Nonlinear Schrodinger Equation and Bogoliubov Excitations for Bose Gases

Phan Thanh, Nam and 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

Abstract

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Analysis, Mathematical Physics and Numerics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0010-3616
• Language: English