Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems Journal Article

Author(s): Lundholm, Douglas; Nam, Phan Thanh; Portmann, Fabian
Article Title: Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems
Affiliation IST Austria
Abstract: 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.
Journal Title: Archive for Rational Mechanics and Analysis
Volume: 219
Issue 3
ISSN: 1432-0673
Publisher: Springer  
Date Published: 2016-03-01
Start Page: 1343
End Page: 1382
DOI: 10.1007/s00205-015-0923-5
Notes: We thank Jan Philip Solovej , Robert Seiringer and Vladimir Maz’ya for helpful discussions, as well as Rupert Frank and the anonymous referee for useful comments. Part of this work has been carried out during a visit at the Institut Mittag- Leffler (Stockholm). D.L. acknowledges financial support by the grant KAW 2010.0063 from the Knut and Alice Wallenberg Foundation and the Swedish Research Council grant no. 2013-4734. P.T.N. is supported by the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme (FP7/2007-2013) under REA grant agreement no. 291734. F.P. acknowledges support from the ERC project no. 321029 “The mathematics of the structure of matter”.
Open access: yes (repository)
IST Austria Authors
  1. Phan Thanh Nam
    12 Nam
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