Non-existence of a Hohenberg-Kohn Variational Principle in Total Current Density Functional Theory

• 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).

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

NATURVETENSKAP  -- Fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences (hsv//eng)

Keyword

Current density functional theory

Hohenberg-Kohn variational principle

total current density

Mathematics

Matematik

Publication and Content Type

vet (subject category)

art (subject category)