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Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-3456-5846
2016 (English)In: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 219, no 3, p. 1343-1382Article in journal (Refereed) Published
Abstract [en]

We prove analogues of the Lieb-Thirring and Hardy-Lieb-Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 219, no 3, p. 1343-1382
Keywords [en]
Lieb-Thirring inequality, many-body quantum mechanics, uncertainty principle, exclusion principle, interpolation inequality, fractional Laplacian
National Category
Mathematical Analysis
Research subject
Mathematics; Physics
Identifiers
URN: urn:nbn:se:kth:diva-176067DOI: 10.1007/s00205-015-0923-5ISI: 000368535400010Scopus ID: 2-s2.0-84954367932OAI: oai:DiVA.org:kth-176067DiVA, id: diva2:865921
Projects
VR 2013-4734: Spectral theory of quantum systems with exotic symmetries
Funder
Swedish Research Council, 67801Knut and Alice Wallenberg Foundation, KAW 2010.0063EU, European Research Council, 321029Swedish Research Council, 2013-4734
Note

QC 20160220

Available from: 2015-10-29 Created: 2015-10-29 Last updated: 2017-12-01Bibliographically approved

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Lundholm, Douglas

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