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Annales Henri Poincaré

, Volume 15, Issue 6, pp 1061–1107 | Cite as

Local Exclusion and Lieb–Thirring Inequalities for Intermediate and Fractional Statistics

  • Douglas LundholmEmail author
  • Jan Philip Solovej
Article

Abstract

In one and two spatial dimensions there is a logical possibility for identical quantum particles different from bosons and fermions, obeying intermediate or fractional (anyon) statistics. We consider applications of a recent Lieb–Thirring inequality for anyons in two dimensions, and derive new Lieb–Thirring inequalities for intermediate statistics in one dimension with implications for models of Lieb–Liniger and Calogero–Sutherland type. These inequalities follow from a local form of the exclusion principle valid for such generalized exchange statistics.

Keywords

Ground State Energy Fractional Statistics Identical Particle Kinetic Energy Operator Littlewood Maximal Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Authors and Affiliations

  1. 1.Institut Mittag-LefflerDjursholmSweden
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenCopenhagen ØDenmark

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