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...
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Published in | Communications in mathematical physics Vol. 375; no. 1; pp. 495 - 571 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Berlin/Heidelberg
Springer Berlin Heidelberg
01.04.2020
Springer Nature B.V |
Subjects | |
Online Access | Get full text |
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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. |
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ISSN: | 0010-3616 1432-0916 |
DOI: | 10.1007/s00220-019-03480-x |