Lieb–Thirring inequalities for wave functions vanishing on the diagonal set

Larson, Simon; Lundholm, Douglas; Nam, Phan Thành

doi:10.5802/ahl.72

Larson, Simon ¹; Lundholm, Douglas ²; Nam, Phan Thành ³

¹ Department of Mathematics, California Institute of Technology, Pasadena, CA 91125, (USA)
² Department of Mathematics, Uppsala University, Box 480, SE-751 06 Uppsala, (Sweden)
³ Department of Mathematics, LMU Munich, Theresienstrasse 39, 80333 Munich, (Germany)

Annales Henri Lebesgue, Volume 4 (2021), pp. 251-282.

Abstract
Résumé

We propose a general strategy to derive Lieb–Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb–Thirring inequality to wave functions vanishing on the diagonal set of the configuration space, without any statistical assumption on the particles.

Nous proposons une stratégie générale pour démontrer les inégalités de Lieb–Thirring pour des systèmes quantiques à beaucoup de particules, invariant par changement d’échelle. Comme application, nous obtenons une généralisation de l’inégalité de Lieb–Thirring pour les fonctions d’ondes qui s’annulent sur la diagonale de l’espace des configurations, sans aucune hypothèse statistique sur les particules.

Received: 2019-05-12
Accepted: 2020-05-07
Published online: 2021-01-18

DOI: 10.5802/ahl.72

Classification: 81V70, 35R11, 46E35, 81Q10
Mots-clés : Lieb–Thirring inequalities, uncertainty principle, exclusion principle, Poincaré inequality

Author's affiliations:

Larson, Simon ¹; Lundholm, Douglas ²; Nam, Phan Thành ³

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     title = {Lieb{\textendash}Thirring inequalities for wave functions vanishing on the diagonal set},
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Larson, Simon; Lundholm, Douglas; Nam, Phan Thành. Lieb–Thirring inequalities for wave functions vanishing on the diagonal set. Annales Henri Lebesgue, Volume 4 (2021), pp. 251-282. doi : 10.5802/ahl.72. http://www.numdam.org/articles/10.5802/ahl.72/

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