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arXiv · 2002.04963

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

David Gontier·Mathieu Lewin·Faizan Q. Nazar
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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 $d\geq1$. 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.

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David Gontier, Mathieu Lewin, Faizan Q. Nazar. 2021-03-17. The nonlinear Schrödinger equation for orthonormal functions: I. Existence of ground states. https://doi.org/10.1007/s00205-021-01634-7

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