Current Densities in Density Functional Theory

Abstract

It is well known that any given density rho(x)can be realized by a determinantal wave function for N particles. The question addressed here is whether any given density rho(x) and current density j(x) can be simultaneously realized by a (finite kinetic energy) determinantal wave function. In case the velocity field v(x) =j(x)/rho(x) is curl free, we provide a solution for all N, and we provide an explicit upper bound for the energy. If the velocity field is not curl free, there is a finite energy solution for all N\geq 4, but we do not provide an explicit energy bound in this case. For N=2 we provide an example of a non curl free velocity field for which there is a solution, and an example for which there is no solution. The case $N=3 with a non curl free velocity field is left open.

21 pages, latex, reference added

Cited by in corpus (12)

• Existence, Uniqueness, and Construction of the Density-Potential Mapping in Time-Dependent Density-Functional Theory
• Statistical Mechanics of the Uniform Electron Gas
• Uniform magnetic fields in density-functional theory
• Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
• Fermion $N$-representability for prescribed density and paramagnetic current density
• The structure of the density-potential mapping. Part II: Including magnetic fields
• A local tensor that unifies kinetic energy density and vorticity dependent exchange-correlation functionals
• Metric space approach to potentials and its relevance to density functional theory
• Metric space analysis of systems immersed in a magnetic field
• Pure-state $N$-representability in current-spin-density-functional theory
• Regularity of the (N-1)-particle electronic reduced density matrix for molecules with fixed nuclei and N electrons
• Mixed state representability of entropy-density pairs