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Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems

Archive for Rational Mechanics and Analysis volume 219, pages 1343–1382 (2016)Cite this article

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.

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Authors and Affiliations

  1. KTH Royal Institute of Technology, Stockholm, Sweden

    Douglas Lundholm

  2. Institute of Science and Technology Austria, Klosterneuburg, Austria

    Phan Thành Nam

  3. University of Copenhagen, Copenhagen, Denmark

    Fabian Portmann

Authors
  1. Douglas Lundholm
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  2. Phan Thành Nam
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  3. Fabian Portmann
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Correspondence to Phan Thành Nam.

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Communicated by C. Le Bris

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Lundholm, D., Nam, P.T. & Portmann, F. Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems. Arch Rational Mech Anal 219, 1343–1382 (2016). https://doi.org/10.1007/s00205-015-0923-5

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  • DOI: https://doi.org/10.1007/s00205-015-0923-5

Keywords

  • Phan
  • Hardy Inequality
  • Relate Inequality
  • Interpolation Inequality
  • Local Uncertainty