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

D. Lundholm, P. Nam, F. Portmann, Archive for Rational Mechanics and Analysis 219 (2016) 1343–1382.


Journal Article | Published | English
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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.
Publishing Year
Date Published
2016-03-01
Journal Title
Archive for Rational Mechanics and Analysis
Acknowledgement
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”.
Volume
219
Issue
3
Page
1343 - 1382
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Cite this

Lundholm D, Nam P, Portmann F. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. 2016;219(3):1343-1382. doi:10.1007/s00205-015-0923-5
Lundholm, D., Nam, P., & Portmann, F. (2016). Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis, 219(3), 1343–1382. https://doi.org/10.1007/s00205-015-0923-5
Lundholm, Douglas, Phan Nam, and Fabian Portmann. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis 219, no. 3 (2016): 1343–82. https://doi.org/10.1007/s00205-015-0923-5.
D. Lundholm, P. Nam, and F. Portmann, “Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems,” Archive for Rational Mechanics and Analysis, vol. 219, no. 3, pp. 1343–1382, 2016.
Lundholm D, Nam P, Portmann F. 2016. Fractional Hardy–Lieb–Thirring and related Inequalities for interacting systems. Archive for Rational Mechanics and Analysis. 219(3), 1343–1382.
Lundholm, Douglas, et al. “Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems.” Archive for Rational Mechanics and Analysis, vol. 219, no. 3, Springer, 2016, pp. 1343–82, doi:10.1007/s00205-015-0923-5.

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