Abstract
Local effective potential theory, both stationary-state and time-dependent, constitutes the mapping from a system of electrons in an external field to one of the noninteracting fermions possessing the same basic variable such as the density, thereby enabling the determination of the energy and other properties of the electronic system. This paper is a description via Quantal Density Functional Theory (QDFT) of the electron correlations that must be accounted for in such a mapping. It is proved through QDFT that independent of the form of external field, (a) it is possible to map to a model system possessing all the basic variables; and that (b) with the requirement that the model fermions are subject to the same external fields, the only correlations that must be considered are those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects. The cases of both a static and time-dependent electromagnetic field, for which the basic variables are the density and physical current density, are considered. The examples of solely an external electrostatic or time-dependent electric field constitute special cases. An efficacious unification in terms of electron correlations, independent of the type of external field, is thereby achieved. The mapping is explicated for the example of a quantum dot in a magnetostatic field, and for a quantum dot in a magnetostatic and time-dependent electric field.
Highlights
This paper is concerned with the electron correlations within local effective potential theory (LEPT) such as Kohn–Sham [1] (KS) and Quantal (Q) [2,3] density functional theory (DFT).We begin with a brief description of the electron correlations that must be accounted for withinLEPT
In recent work [12], we have proved that the basic variables for the physical system described above, in which the interaction of the magnetic field is solely with the orbital angular momentum, are the nondegenerate ground state density ρ(r) and the physical current density j(r)
The Quantal density functional theory (QDFT) equations for the local potential vee (r) and total energy E show that for electrons in an external static electric and magnetic field it is (a) possible to map to a model system of noninteracting fermions possessing the same basic variables {ρ(r), j(r)}; and (b) that the only correlations that need to be considered in the mapping are those of the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects
Summary
This paper is concerned with the electron correlations within local effective potential theory (LEPT) such as Kohn–Sham [1] (KS) and Quantal (Q) [2,3] density functional theory (DFT). In time-dependent LEPT, such as Runge–Gross (RG) [11] DFT or QDFT [4], the electrons are subject to a time-dependent external field E (rt) = −∇v(rt) In this case, as proved by the RG theorem [11], a basic variable is the density ρ(rt). Via QDFT, a generalization of all LEPT such that the only correlations that need to be accounted for are solely those due to the Pauli exclusion principle, Coulomb repulsion, and Correlation–Kinetic effects. This requires that the noninteracting fermions (a) possess all the basic variables; and (b) be subject to the same external fields as those of the interacting system.
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