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

Institut for Matematiske Fag

22 Citationer (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.

Originalsprog	Engelsk
Tidsskrift	Communications in Mathematical Physics
Vol/bind	322
Udgave nummer	3
Sider (fra-til)	883-908
ISSN	0010-3616
DOI	https://doi.org/10.1007/s00220-013-1748-4
Status	Udgivet - sep. 2013

Adgang til dokumentet

10.1007/s00220-013-1748-4

http://arxiv.org/abs/1108.5129

Citationsformater

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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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N2 - 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.

AB - 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.

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