2017/06/18 by Codina Cotar, Gero Friesecke, Claudia Klüppelberg · 53 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Combinatorics #Coulomb #Counterexample #Electron #Geometry #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quadratic equation #Quantum mechanics #Semiclassical physics #Smoothing #Spectroscopy and Quantum Chemical Studies #Wave function #math-ph #math.AP #math.MP #nanoparticles nucleation surface interactions #quant-ph
paper · pdf · doi:10.1007/s00205-017-1208-y
published in Archive for Rational Mechanics and Analysis 228(3), 891-922 (Springer Science+Business Media)
arxiv created 2017/06/18 · openalex publication_date 2018/02/20 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove rigorously that the exact N-electron Hohenberg-Kohn density functional converges in the strongly interacting limit to the strictly correlated electrons (SCE) functional, and that the absolute value squared of the associated constrained-search wavefunction tends weakly in the sense of probability measures to a minimizer of the multi-marginal optimal transport problem with Coulomb cost associated to the SCE functional. This extends our previous work for N=2 [CFK11]. The correct limit problem has been derived in the physics literature by Seidl [Se99] and Seidl, Gori-Giorgi and Savin [SGS07]; in these papers the lack of a rigorous proof was pointed out. We also give a mathematical counterexample to this type of result, by replacing the constraint of given one-body density -- an infinite-dimensional quadratic expression in the wavefunction -- by an infinite-dimensional quadratic expression in the wavefunction and its gradient. Connections with the Lawrentiev phenomenon in the calculus of variations are indicated.