Local-energy density functionals for an N-dimensional electronic system in a magnetic field

TL;DR

This paper develops a comprehensive method to construct exact local-energy-density functionals for N-dimensional electronic systems in magnetic fields, extending Thomas-Fermi theory and enabling current-density-functional analysis of inhomogeneous systems.

Contribution

It introduces explicit expressions for energy functionals in arbitrary dimensions and formulates a current-density-functional theory for inhomogeneous systems in magnetic fields.

Findings

Derived explicit energy functionals for arbitrary dimensions.

Recovered classical Thomas-Fermi theory in zero magnetic field.

Formulated a current-density-functional theory for inhomogeneous systems.

Abstract

We present a general approach for the construction of the exact local-energy-density functionals for a uniform N-dimensional electronic system in a magnetic field. For arbitrary dimension, we obtain explicit expressions for the matter, kinetic, and exchange density functionals. In the zero-field limit, we recover the usual N-dimensional Thomas-Fermi theory. As an application of our results, we develop a current-density-functional theory, in the spirit of the Thomas-Fermi-Dirac approximation, for an inhomogeneous many-electron system in a magnetic field.