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Article Dans Une Revue Duke Mathematical Journal Année : 2012

A positive density analogue of the Lieb-Thirring inequality

Résumé

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. This is dual to a bound on the $H^1$-norms of a system of orthonormal functions. Here we extend these to analogous inequalities for perturbations of the Fermi sea of non-interacting particles, i.e., for perturbations of the continuous spectrum of the Laplacian by local potentials.

Dates et versions

hal-00616552 , version 1 (23-08-2011)

Identifiants

Citer

Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer. A positive density analogue of the Lieb-Thirring inequality. Duke Mathematical Journal, 2012, 162 (3), pp.435--495. ⟨10.1215/00127094-2019477⟩. ⟨hal-00616552⟩
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