A positive density analogue of the Lieb–Thirring inequality

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 H^1-norms of a system of orthonormal functions. Here we extend these bounds to analogous inequalities for perturbations of th...

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Bibliographic Details
Published in:Duke Mathematical Journal
Main Authors: Frank, Rupert L., Lewin, Mathieu, Lieb, Elliott H., Seiringer, Robert
Format: Article in Journal/Newspaper
Language:unknown
Published: Duke University Press 2013
Subjects:
Ari
laptev
Online Access:https://doi.org/10.1215/00127094-2019477
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Summary: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 H^1-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). © 2013 Duke University Press. Received 4 September 2011. Revision received 1 March 2012. Frank's work partially supported by National Science Foundation grant PHY-1068285. Lewin's work partially supported by European Research Council grant MNIQS-258023. Lieb's work partially supported by National Science Foundation grant PHY-0965859. Seiringer's work partially supported by the Natural Sciences and Engineering Research Council. The first author would like to thank Ari Laptev for stimulating discussions. Submitted - 1108.4246.pdf

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