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- Laestadius, André, 1984-, et al.
(författare)
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Hohenberg-Kohn Theorems in the Presence of Magnetic Field
- 2014
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Ingår i: International Journal of Quantum Chemistry. - : John Wiley & Sons. - 0020-7608 .- 1097-461X. ; 114:12, s. 782-795
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we examine Hohenberg-Kohn theorems for Current Density Functional Theory, that is, generalizations of the classical Hohenberg-Kohn theorem that includes both electric and magnetic fields. In the Vignale and Rasolt formulation (Vignale and Rasolt, Phys. Rev. Lett. 1987, 59, 2360), which uses the paramagnetic current density, we address the issue of degenerate ground states and prove that the ensemble-representable particle and paramagnetic current density determine the degenerate ground states. For the formulation that uses the total current density, we note that the proof suggested by Diener (Diener, J. Phys.: Condens. Matter. 1991, 3, 9417) is unfortunately not correct. Furthermore, we give a proof that the magnetic field and the ensemble-representable particle density determine the scalar and vector potentials up to a gauge transformation. This generalizes the result of Grayce and Harris (Grayce and Harris, Phys. Rev. A 1994, 50, 3089) to the case of degenerate ground states. We moreover prove the existence of a positive wavefunction that is the ground state of infinitely many different Hamiltonians.
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| 2. |
- Laestadius, Andre, 1984-, et al.
(författare)
-
Non-existence of a Hohenberg-Kohn Variational Principle in Total Current Density Functional Theory
- 2015
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Ingår i: Physical Review A. Atomic, Molecular, and Optical Physics. - 1050-2947 .- 1094-1622. ; 91:3
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)abstract
- For a many-electron system, whether the particle density rho and the total current density j are sufficient to determine the one-body potential V and vector potential A, is still an open question. For the one-electron case, a Hohenberg-Kohn theorem exists formulated with the total current density. Here we show that the generalized Hohenberg-Kohn energy functional E_{V_0,A_0}(rho,j) = can be minimal for densities that are not the ground-state densities of the fixed potentials V_0 and A_0. Furthermore, for an arbitrary number of electrons and under the assumption that a Hohenberg-Kohn theorem exists formulated with rho and j, we show that a variational principle for Total Current Density Functional Theory as that of Hohenberg-Kohn for Density Functional Theory does not exist. The reason is that the assumed map from densities to the vector potential, written (rho,j) -> A(rho,j;x), enters explicitly in E_{V_0,A_0}(rho,j).
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