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

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• 作者：Douglas Lundholm ; Phan Thành Nam…
• 刊名：Archive for Rational Mechanics and Analysis
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：219
• 期：3
• 页码：1343-1382
• 全文大小：783 KB
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• 作者单位：Douglas Lundholm (1)
  Phan Thành Nam (2)
  Fabian Portmann (3)
  
  1. KTH Royal Institute of Technology, Stockholm, Sweden
  2. Institute of Science and Technology Austria, Klosterneuburg, Austria
  3. University of Copenhagen, Copenhagen, Denmark
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Mechanics
  Electromagnetism, Optics and Lasers
  Mathematical and Computational Physics
  Complexity
  Fluids
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0673

文摘

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. Communicated by C. Le Bris