An Optimal Minimization Problem in the Lowest Landau Level and Related Questions

We solve a minimization problem related to the cubic Lowest Landau level equation, which is used in the study of Bose–Einstein condensation. We provide an optimal condition for the Gaussian to be the unique global minimizer. This extends previous results from P. Gérard, P. Germain and L. Thomann. We...

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Bibliographic Details
Published in:Communications in mathematical physics 2024-04, Vol.405 (4), Article 98
Main Author: Schwinte, Valentin
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Mathematical and Computational Physics
Mathematical Physics
Optimization
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We solve a minimization problem related to the cubic Lowest Landau level equation, which is used in the study of Bose–Einstein condensation. We provide an optimal condition for the Gaussian to be the unique global minimizer. This extends previous results from P. Gérard, P. Germain and L. Thomann. We then provide another condition so that the second special Hermite function is a global minimizer.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-024-04974-z