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

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.042518· OSTI ID:21544625

Tao, Yang; Xiaoyin, Pan; Sahni, Viraht ^[1]

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1. Department of Physics and Institute of Modern Physics, Ningbo University, Ningbo 315211 (China)

We generalize the quantal density-functional theory (QDFT) of electrons in the presence of an external electrostatic field E(r)=-{nabla}v(r) to include an external magnetostatic field B(r)={nabla}xA(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 {rho}(r) and physical current density j(r), and from which the total energy can be obtained. The properties ({rho}(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.

• OSTI ID: 21544625
• Journal Information: Physical Review. A, Vol. 83, Issue 4; Other Information: DOI: 10.1103/PhysRevA.83.042518; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ATOMS
CURRENT DENSITY
DENSITY
DENSITY FUNCTIONAL METHOD
ELECTRONS
EXACT SOLUTIONS
EXCITED STATES
HOOKE LAW
MAGNETIC FIELDS
MAPPING
POTENTIALS
QUANTUM MECHANICS
THREE-DIMENSIONAL CALCULATIONS
TWO-DIMENSIONAL CALCULATIONS
CALCULATION METHODS
ELEMENTARY PARTICLES
ENERGY LEVELS
FERMIONS
LEPTONS
MATHEMATICAL SOLUTIONS
MECHANICS
PHYSICAL PROPERTIES
VARIATIONAL METHODS