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General decomposition of radial functions on \(\mathbb R^n\) and applications to \(N\)-body quantum systems. (English) Zbl 1016.81059

Summary: We present a generalization of the Fefferman-de la Llave decomposition of the Coulomb potential to quite arbitrary radial functions \(V\) on \(\mathbb R^n\) 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.

MSC:

81V70 Many-body theory; quantum Hall effect
42A82 Positive definite functions in one variable harmonic analysis
46N50 Applications of functional analysis in quantum physics
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