Symmetry breaking regime in the nonlinear Hartree equation

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Abstract
The present paper is concerned with minimizers \Phi of the Hartree energyfunctional H g [ /; /] =2 + (/; v/) 2 + g(/; V j/j/) 2 with g ! 0 onthe configuration space R, d 2, for a general class of external potentials vand two-body potentials V . We prove that a minimizer \Phi does not have thesymmetry properties of the potential v for jgj strictly larger than a criticalg ? 0. A numerical investigation visualizes this symmetry breaking regimein the simple case of an...