Fractional Hardy-Lieb-Thirring and related inequalities for interacting systems

TL;DR

This paper establishes new inequalities for many-body quantum systems with fractional kinetic energy and interaction potentials, extending classical results without requiring wave function anti-symmetry, and explores their equivalence to one-body inequalities.

Contribution

It introduces fractional Hardy-Lieb-Thirring inequalities for interacting systems, generalizing existing inequalities to fractional operators and demonstrating their equivalence to one-body inequalities.

Findings

Proved fractional Hardy-Lieb-Thirring inequalities for many-body systems.

Established the equivalence between one- and many-body inequalities in certain cases.

Extended classical inequalities to fractional kinetic operators and homogeneous interactions.

Abstract

We prove analogues of the Lieb-Thirring and Hardy-Lieb-Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no anti-symmetry on the wave functions is assumed. These many-body inequalities imply interesting one-body interpolation inequalities, and we show that the corresponding one- and many-body inequalities are actually equivalent in certain cases.