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

Tao Yang, Xiao-Yin Pan, Viraht Sahni
2011 Physical Review A. Atomic, Molecular, and Optical Physics  
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
more » ... 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 (2-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 semi-analytical form. A comparison with the corresponding mapping from a ground state of the (3-dimensional) Hooke's atom in the absence of a magnetic field is also made.
doi:10.1103/physreva.83.042518 fatcat:bedp5dpovfav7olztai2hsgcui