Symmetry breaking for Schr\"odinger-Poisson-Slater energy

TL;DR

This paper investigates the asymptotic behavior of the ground state energy in Schr"odinger-Poisson-Slater systems, revealing that symmetry restrictions influence energy levels as particle numbers grow large.

Contribution

It demonstrates that restricting to radially symmetric functions results in higher ground state energy for large particle numbers, highlighting symmetry effects in these systems.

Findings

Radial symmetry restriction increases ground state energy at large particle counts

Asymptotic analysis of Schr"odinger-Poisson-Slater energy functional

Symmetry considerations impact energy minimization in quantum systems

Abstract

We study the asymptotic behavior of ground state energy for Schr\"odinger-Poisson-Slater energy functional. We show that ground state energy restricted to radially symmetric functions is above the ground state energy when the number of particles is sufficiently large.