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 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).

Original languageEnglish (US)
Pages (from-to)435-495
Number of pages61
JournalDuke Mathematical Journal
Volume162
Issue number3
DOIs
StatePublished - Feb 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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    Frank, R. L., Lewin, M., Lieb, E. H., & Seiringer, R. (2013). A positive density analogue of the lieb-thirring inequality. Duke Mathematical Journal, 162(3), 435-495. https://doi.org/10.1215/00127094-2019477