Quantal density-functional theory in the presence of a magnetic field

Abstract

We generalize the quantal density-functional theory (QDFT) of electrons in the presence of an external electrostatic field E(r)=-v(r) to include an external magnetostatic field B(r)=×A(r), where {v(r),A(r)} are the respective scalar and vector potentials. The generalized QDFT, valid for nondegenerate ground and excited states, is the mapping from the interacting system of electrons to a model of noninteracting fermions with the same density ρ(r) and physical current density j(r), and from which the total energy can be obtained. The properties {ρ(r),j(r)} constitute the basic quantum-mechanical variables because, as proved previously, for a nondegenerate ground state they uniquely determine the potentials {v(r),A(r)}. The mapping to the noninteracting system is arbitrary in that the model fermions may be either in their ground or excited state. The theory is explicated by application to a ground state of the exactly solvable (two-dimensional) Hooke's atom in a magnetic field, with the mapping being to a model system also in its ground state. The majority of properties of the model are obtained in closed analytical or semianalytical form. A comparison with the corresponding mapping from a ground state of the (three-dimensional) Hooke's atom in the absence of a magnetic field is also made. © 2011 American Physical Society.