The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states

Abstract

We study the nonlinear Schrödinger equation for systems of $N$ orthonormal functions. We prove the existence of ground states for all $N$ when the exponent $p$ of the non linearity is not too large, and for an infinite sequence $N_j$ tending to infinity in the whole range of possible $p$'s, in dimensions $d\ge 1$. This allows us to prove that translational symmetry is broken for a quantum crystal in the Kohn-Sham model with a large Dirac exchange constant.

Final version, to appear in Arch. Rat. Mech. Anal

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• Geometric methods for nonlinear many-body quantum systems
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Cited by in corpus (3)

• The nonlinear Schrödinger equation for orthonormal functions: II. Application to Lieb-Thirring inequalities
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• Thermodynamic Limits of Electronic Systems