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

Phan Thanh, Nam und Salzmann, Robert (2020): Derivation of 3D Energy-Critical Nonlinear Schrodinger Equation and Bogoliubov Excitations for Bose Gases. In: Communications in Mathematical Physics, Bd. 375, Nr. 1: S. 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.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0010-3616
• Sprache: Englisch