Symmetry breaking in the self-consistent Kohn–Sham equations

2005/02/28 by E. Prodan, E Prodan
Chemistry · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Cold Atom Physics and Bose-Einstein Condensates #Quantum many-body systems #cond-mat.stat-mech #math-ph #math.MP #physics.chem-ph #physics.comp-ph

paper · pdf · doi:10.1088/0305-4470/38/25/004

published as J. Phys. A: Math. and Gen. 38, 5647-5657 (2005) · a few typos eliminated

arxiv created 2005/06/08 · openalex publication_date 2005/06/08 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

The Kohn–Sham (KS) equations determine, in a self-consistent way, the particle density of an interacting fermion system at thermal equilibrium. We consider a situation when the KS equations are known to have a unique solution at high temperatures and that this solution is a uniform particle density. We prove that, at zero temperature, there are stable solutions that are not uniform. We provide the general principles behind this phenomenon, namely the conditions when it can be observed and how to construct these non-uniform solutions. Two concrete examples are provided, including fermions on the sphere which are shown to crystallize in a structure that resembles the C 60 molecule.

Citations

• Self-Consistent Equations Including Exchange and Correlation Effects

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