# Hardy and Lieb-Thirring Inequalities for Anyons

@article{Lundholm2013HardyAL,
title={Hardy and Lieb-Thirring Inequalities for Anyons},
author={Douglas Lundholm and Jan Philip Solovej},
journal={Communications in Mathematical Physics},
year={2013},
volume={322},
pages={883-908}
}
• Published 25 August 2011
• Mathematics
• Communications in Mathematical Physics
We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $${\alpha \in [0, 1]}$$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…
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