The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit

We consider an analogue of the Lieb–Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb–Thirring constant converges to the optimal constant of the...

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Bibliographic Details
Published inArchive for rational mechanics and analysis Vol. 240; no. 3; pp. 1169 - 1202
Main Authors Kögler, Kevin, Nam, Phan Thành
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2021
Springer Nature B.V
Subjects
Antisymmetry
Classical Mechanics
Complex Systems
Coupling
Fluid- and Aerodynamics
Inequality
Interpolation
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
Wave functions
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Summary:We consider an analogue of the Lieb–Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb–Thirring constant converges to the optimal constant of the one-body Gagliardo–Nirenberg interpolation inequality without interaction.
ISSN:0003-9527
1432-0673
DOI:10.1007/s00205-021-01633-8