Hardy and Lieb-Thirring Inequalities for Anyons

Douglas Björn Alexander Lundholm; Jan Philip Solovej

doi:10.1007/s00220-013-1748-4

Hardy and Lieb-Thirring Inequalities for Anyons

Douglas Björn Alexander Lundholm, Jan Philip Solovej

Department of Mathematical Sciences

22 Citations (Scopus)

Abstract

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter α∈[0,1] ranging from bosons (α = 0) to fermions (α = 1). We prove a (magnetic) Hardy inequality for anyons, which in the case that α is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by Dyson and Lenard’s original approach to the stability of fermionic matter in three dimensions, we prove a Lieb-Thirring inequality for these types of anyons.

Original language	English
Journal	Communications in Mathematical Physics
Volume	322
Issue number	3
Pages (from-to)	883-908
ISSN	0010-3616
DOIs	https://doi.org/10.1007/s00220-013-1748-4
Publication status	Published - Sept 2013

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10.1007/s00220-013-1748-4

http://arxiv.org/abs/1108.5129

Cite this

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title = "Hardy and Lieb-Thirring Inequalities for Anyons",

abstract = "We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter α∈[0,1] ranging from bosons (α = 0) to fermions (α = 1). We prove a (magnetic) Hardy inequality for anyons, which in the case that α is an odd numerator fraction implies a local exclusion principle for the kinetic energy of such anyons. From this result, and motivated by Dyson and Lenard{\textquoteright}s original approach to the stability of fermionic matter in three dimensions, we prove a Lieb-Thirring inequality for these types of anyons.",

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DO - 10.1007/s00220-013-1748-4

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