Density functionals in the presence of magnetic field

• In this article, density functionals for Coulomb systems subjected to electric and magnetic fields are developed. The density functionals depend on the particle density rho and paramagnetic current density j(p). This approach is motivated by an adapted version of the Vignale and Rasolt formulation of current density functional theory, which establishes a one-toone correspondence between the nondegenerate groundstate and the particle and paramagnetic current density. Definition of N-representable density pairs (rho,j(p)) is given and it is proven that the set of v-representable densities constitutes a proper subset of the set of N-representable densities. For a Levy-Lieb-type functional Q(rho,j(p)), it is demonstrated that (i) it is a proper extension of the universal Hohenberg-Kohn functional F-HK (rho,j(p)) to N-representable densities, (ii) there exists a wavefunction psi(0) such that Q(rho; j(p)) = (psi(0); H-0 psi(0))(rho), where H-0 is the Hamiltonian without external potential terms, and (iii) it is not convex. Furthermore, a convex and universal functional F(rho, j(p)) is studied and proven to be equal the convex envelope of Q(rho, j(p)). For both Q and F, we give upper and lower bounds.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

current density functional theory

paramagnetic current density functionals

Levy-Lieb density functional

convexity

Euler-Lagrange equations

Mathematics

Matematik

Publikations- och innehållstyp

ref (ämneskategori)

art (ämneskategori)