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

TL;DR

This paper establishes a Lieb-Thirring inequality for a quantum particle model with point interactions of infinite scattering length, providing bounds on the energy based on particle density.

Contribution

It proves a Lieb-Thirring inequality for fermions with point interactions of infinite scattering length, a novel result in quantum many-body theory.

Findings

Energy is bounded below by a constant times the density to the power 5/3

Validates the Lieb-Thirring inequality for this specific interaction model

Advances understanding of quantum particles with singular 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.