Lieb-Thirring Inequality for a Model of Particles with Point Interactions

Abstract

We consider a model of quantum-mechanical particles interacting via point interactions of infinite scattering length. In the case of fermions we prove a Lieb-Thirring inequality for the energy, i.e., we show that the energy is bounded from below by a constant times the integral of the particle density to the power 5/3.

LaTeX, 13 pages

References in corpus (3)

• Critical Temperature and Thermodynamics of Attractive Fermions at Unitarity
• Thermodynamics of balanced and slightly spin-imbalanced Fermi gases at unitarity
• Hardy and Lieb-Thirring inequalities for anyons

Cited by in corpus (12)

• Stability for a System of N Fermions Plus a Different Particle with Zero-Range Interactions
• Hardy and Lieb-Thirring inequalities for anyons
• Local exclusion principle for identical particles obeying intermediate and fractional statistics
• Local exclusion and Lieb-Thirring inequalities for intermediate and fractional statistics
• Exclusion bounds for extended anyons
• Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems
• Lieb-Thirring Bounds for Interacting Bose Gases
• Lieb-Thirring inequality with semiclassical constant and gradient error term
• Fermionic behavior of ideal anyons
• A Lieb-Thirring inequality for extended anyons
• Triviality of a model of particles with point interactions in the thermodynamic limit
• The Lieb-Thirring inequality for interacting systems in strong-coupling limit