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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ftcaltechauth:oai:authors.library.caltech.edu:5ghck-hnt78 2024-09-15T18:17:34+00:00 A positive density analogue of the Lieb–Thirring inequality Frank, Rupert L. Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert 2013-02-15 https://doi.org/10.1215/00127094-2019477 unknown Duke University Press https://doi.org/10.1215/00127094-2019477 https://arxiv.org/abs/1108.4246 oai:authors.library.caltech.edu:5ghck-hnt78 eprintid:37558 resolverid:CaltechAUTHORS:20130319-101032718 info:eu-repo/semantics/openAccess Other Duke Mathematical Journal, 162(3), 435-495, (2013-02-15) info:eu-repo/semantics/article 2013 ftcaltechauth https://doi.org/10.1215/00127094-2019477 2024-08-06T15:35:01Z 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 Article in Journal/Newspaper laptev Caltech Authors (California Institute of Technology) Duke Mathematical Journal 162 3 |
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Caltech Authors (California Institute of Technology) |
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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 |
format |
Article in Journal/Newspaper |
author |
Frank, Rupert L. Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert |
spellingShingle |
Frank, Rupert L. Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert A positive density analogue of the Lieb–Thirring inequality |
author_facet |
Frank, Rupert L. Lewin, Mathieu Lieb, Elliott H. Seiringer, Robert |
author_sort |
Frank, Rupert L. |
title |
A positive density analogue of the Lieb–Thirring inequality |
title_short |
A positive density analogue of the Lieb–Thirring inequality |
title_full |
A positive density analogue of the Lieb–Thirring inequality |
title_fullStr |
A positive density analogue of the Lieb–Thirring inequality |
title_full_unstemmed |
A positive density analogue of the Lieb–Thirring inequality |
title_sort |
positive density analogue of the lieb–thirring inequality |
publisher |
Duke University Press |
publishDate |
2013 |
url |
https://doi.org/10.1215/00127094-2019477 |
genre |
laptev |
genre_facet |
laptev |
op_source |
Duke Mathematical Journal, 162(3), 435-495, (2013-02-15) |
op_relation |
https://doi.org/10.1215/00127094-2019477 https://arxiv.org/abs/1108.4246 oai:authors.library.caltech.edu:5ghck-hnt78 eprintid:37558 resolverid:CaltechAUTHORS:20130319-101032718 |
op_rights |
info:eu-repo/semantics/openAccess Other |
op_doi |
https://doi.org/10.1215/00127094-2019477 |
container_title |
Duke Mathematical Journal |
container_volume |
162 |
container_issue |
3 |
_version_ |
1810455629896089600 |