Dilute Bose gas with three-body interaction: Recent results and open questions

We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schrödinger equation to describe the ground state energy of a Bose–Einstein condensate, where the nonlinearity strength...

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Bibliographic Details
Published in:Journal of Mathematical Physics 2022-06, Vol.63 (6)
Main Authors: Nam, Phan Thành, Ricaud, Julien, Triay, Arnaud
Format: Article
Language:English
Subjects:
Analysis of PDEs
Bose-Einstein condensates
Dilution
Ground state
Mathematical Physics
Mathematics
Physics
Questions
Schrodinger equation
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Summary:We review our recent study on the ground state energy of dilute Bose gases with three-body interactions. The main feature of our results is the emergence of the 3D energy-critical Schrödinger equation to describe the ground state energy of a Bose–Einstein condensate, where the nonlinearity strength is determined by a zero-scattering problem. Several open questions are also discussed.
ISSN:0022-2488
1089-7658
DOI:10.1063/5.0089775