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

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Abstract

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.

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Acknowledgements

The author warmly thanks Laurent Thomann and Pierre Germain for the numerous insightful discussions leading to this work.

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Authors and Affiliations

  1. CNRS, IECL, Université de Lorraine, 54000, Nancy, France

    Valentin Schwinte

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  1. Valentin Schwinte
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Correspondence to Valentin Schwinte.

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Communicated by K. Nakanishi.

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Schwinte, V. An Optimal Minimization Problem in the Lowest Landau Level and Related Questions. Commun. Math. Phys. 405, 98 (2024). https://doi.org/10.1007/s00220-024-04974-z

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