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

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 approxim...

Full description

Saved in:
Bibliographic Details
Published inCommunications in mathematical physics Vol. 375; no. 1; pp. 495 - 571
Main Authors Nam, Phan Thành, Salzmann, Robert
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2020
Springer Nature B.V
Subjects
Approximation
Classical and Quantum Gravitation
Complex Systems
Mathematical analysis
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Schrodinger equation
Theoretical
Wave functions
Online AccessGet full text

Cover

More Information
Summary: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.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-019-03480-x