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arXiv · 1108.4246

A positive density analogue of the Lieb-Thirring inequality

Rupert L. Frank·Mathieu Lewin·Elliott H. Lieb·Robert Seiringer
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Abstract

The Lieb-Thirring inequalities give a bound on the negative eigenvalues of a Schr\"odinger 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.

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Rupert L. Frank, Mathieu Lewin, Elliott H. Lieb, Robert Seiringer. 2011-08-22. A positive density analogue of the Lieb-Thirring inequality. https://doi.org/10.1215/00127094-2019477

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