TY - JOUR

T1 - Current densities in density-functional theory

AU - Lieb, Elliott H.

AU - Schrader, Robert

PY - 2013/9/26

Y1 - 2013/9/26

N2 - 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.

AB - 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.

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U2 - 10.1103/PhysRevA.88.032516

DO - 10.1103/PhysRevA.88.032516

M3 - Article

AN - SCOPUS:84884880779

SN - 1050-2947

VL - 88

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 3

M1 - 032516

ER -