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 $\alpha \in [0,1]$ 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.

Corrected and accepted version. 30 pages, 4 figures

References in corpus (2)

• Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics
• Lieb-Thirring Inequality for a Model of Particles with Point Interactions

Cited by in corpus (26)

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• Local exclusion principle for identical particles obeying intermediate and fractional statistics
• Many-anyon trial states
• Exclusion bounds for extended anyons
• Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems
• A Quantum Impurity Model for Anyons
• Lieb-Thirring Bounds for Interacting Bose Gases
• Lieb-Thirring Inequality for a Model of Particles with Point Interactions
• Lieb-Thirring inequality with semiclassical constant and gradient error term
• Average Field Approximation for Almost Bosonic Anyons in a Magnetic Field
• The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
• Kohn-Sham Density Functional Theory of Abelian Anyons
• Fermionic behavior of ideal anyons
• Hardy-type inequalities for Dunkl operators with applications to many-particle Hardy inequalities
• Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
• Semiclassical limit for almost fermionic anyons
• Properties of 2D anyon gas
• A Lieb-Thirring inequality for extended anyons
• The six blinds and the elephant or an interdisciplinary selection of measurement features
• Triviality of a model of particles with point interactions in the thermodynamic limit
• A simple approach to Lieb--Thirring type inequalities
• The Lieb-Thirring inequality for interacting systems in strong-coupling limit
• A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma
• Natural orbitals and their occupation numbers for free anyons in the magnetic gauge
• Local Quantum Fields for Anyons on the Circle leading to Non-Relativistic Anyons in Two Dimensions
• 2D magnetic stability