Current densities in density-functional theory

Elliott H. Lieb, Robert Schrader

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


It is well known that any given density ρ(x) can be realized by a determinantal wave function for N particles. The question addressed here is whether any given density ρ(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)/ρ(x) is curlfree, 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≥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.

Original languageEnglish (US)
Article number032516
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Issue number3
StatePublished - Sep 26 2013

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics


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