A positive density analogue of the lieb-thirring inequality

Rupert L. Frank; Mathieu Lewin; Elliott H. Lieb; Robert Seiringer

doi:10.1215/00127094-2019477

A positive density analogue of the lieb-thirring inequality

Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer

Mathematics

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25 Scopus citations

Abstract

The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schrödinger operator in terms of an L_p-norm of the potential. These are dual to bounds on the H₁-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of the Fermi sea of noninteracting particles (i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials).

Original language	English (US)
Pages (from-to)	435-495
Number of pages	61
Journal	Duke Mathematical Journal
Volume	162
Issue number	3
DOIs	https://doi.org/10.1215/00127094-2019477
State	Published - Feb 2013

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1215/00127094-2019477

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abstract = "The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr{\"o}dinger operator in terms of an Lp-norm of the potential. These are dual to bounds on the H1-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of the Fermi sea of noninteracting particles (i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials).",

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AU - Lewin, Mathieu

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AU - Seiringer, Robert

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AB - The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schrödinger operator in terms of an Lp-norm of the potential. These are dual to bounds on the H1-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of the Fermi sea of noninteracting particles (i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials).

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A positive density analogue of the lieb-thirring inequality

Abstract

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