Hardy and Lieb-Thirring Inequalities for Anyons

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Douglas Björn Alexander Lundholm, Jan Philip Solovej

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.
OriginalsprogEngelsk
TidsskriftCommunications in Mathematical Physics
Vol/bind322
Udgave nummer3
Sider (fra-til)883-908
ISSN0010-3616
DOI
StatusUdgivet - 2013

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