Hardy and Lieb-Thirring inequalities for anyons

Details Hardy and Lieb-Thirring inequalities for anyons Hardy and Lieb-Thirring inequalities for anyons

2011-08-25

arxiv.org/abs/1108.5129v1

Mathematics

Spectral Theory

29 pages, 4 figures

Scientific paper

We consider the many-particle quantum mechanics of anyons, i.e. identical particles in two space dimensions with a continuous statistics parameter $\alpha \in [0,1]$ ranging from bosons ($\alpha=0$) to fermions ($\alpha=1$). We prove a (magnetic) Hardy inequality for anyons, which in the case that $\alpha$ 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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