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Universal diagonal estimates for minimizers of the Levy–Lieb functional

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Abstract

Given a wave-function minimizing the Levy–Lieb functional, the intent of this short note is to give an estimate of the probability of the particles being in positions \((x_1, \ldots , x_N)\) in the \(\delta \)-close regime \(D_{\delta }= \cup _{i \ne j} \{|x_i - x_j| \le \delta \}\).

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Acknowledgements

Part of this work has been developed during a Research in Pairs program where the authors were hosted at the MFO (Mathematisches Forschungsinstitut Oberwolfach) in January 2017. S.D.M. is a member of GNAMPA (INdAM) and acknowledges the support of the AFOSR project FA8655-22-1-7034. A.G. acknowledges partial support of his research by the Canada Research Chairs Program and Natural Sciences and Engineering Research Council of Canada. L.N. is partially on academic leave at Inria (team Matherials) for the year 2022–2023 and acknowledges the hospitality if this institution during this period. His work was supported by a public grant as part of the Investissement d’avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH and from H-Code, Université Paris-Saclay. The authors want to thank M. Lewin for comments (and references) on a preliminary draft of the paper. They are also indebted to two anonymous referees for their many insightful comments on an earlier draft of this work.

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Authors and Affiliations

  1. MaLGA, Università degli Studi di Genova (DIMA), Genoa, Italy

    S. Di Marino

  2. Department of Mathematics and Statistics, University of Ottawa, Ottawa, Canada

    A. Gerolin

  3. Department of Chemistry and Biomolecular Sciences, University of Ottawa, Ottawa, Canada

    A. Gerolin

  4. Laboratoire de mathématiques d’Orsay, CNRS, Université Paris-Saclay, 91405, Orsay, France

    L. Nenna

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Di Marino, S., Gerolin, A. & Nenna, L. Universal diagonal estimates for minimizers of the Levy–Lieb functional. Lett Math Phys 113, 105 (2023). https://doi.org/10.1007/s11005-023-01729-0

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