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

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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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