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    Degenerate ground states and nonunique potentials: Breakdown and restoration of density functionals

    Capelle, K.
    Ullrich, Carsten A.
    Vignale, Giovanni, 1957-
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    [PDF] DegenerateGroundStatesNonunique.pdf (97.68Kb)
    Date
    2007
    Format
    Article
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    Abstract
    The Hohenberg-Kohn (HK) theorem is one of the most fundamental theorems of quantum mechanics, and constitutes the basis for the very successful density-functional approach to inhomogeneous interacting many-particle systems. Here we show that in formulations of density-functional theory (DFT) that employ more than one density variable, applied to systems with a degenerate ground state, there is a subtle loophole in the HK theorem, as all mappings between densities, wave functions, and potentials can break down. Two weaker theorems which we prove here, the joint-degeneracy theorem and the internal-energy theorem, restore the internal, total, and exchange-correlation energy functionals to the extent needed in applications of DFT to atoms, molecules, and solids. The joint-degeneracy theorem constrains the nature of possible degeneracies in general many-body systems.
    URI
    http://hdl.handle.net/10355/7601
    Citation
    Phys. Rev. A 76, 012508 (2007)
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    • Physics and Astronomy publications (MU)

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