General Decomposition of Radial Functions on R^n and Applications to N-Body Quantum Systems

TL;DR

This paper generalizes a mathematical decomposition technique for radial functions on R^n, enabling the extension of quantum N-body system results from Coulomb to more general interactions, exemplified by Yukawa potential analysis.

Contribution

It introduces a broad generalization of the Fefferman-de la Llave decomposition, applicable to various radial functions, facilitating new analyses in quantum many-body physics.

Findings

Derived high density asymptotics of jellium with Yukawa interaction

Extended N-body quantum system results to general radial potentials

Utilized correlation estimates for energy analysis

Abstract

We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions $V$ on $R^n$ going to zero at infinity. This generalized decomposition can be used to extend previous results on $N$-body quantum systems with Coulomb interaction to a more general class of interactions. As an example of such an application we derive the high density asymptotics of the ground state energy of jellium with Yukawa interaction in the thermodynamic limit, using a correlation estimate by Graf and Solovej.