Related papers: Hohenberg-Kohn Theorems in Electrostatic and Unifo…
The Hohenberg-Kohn theorem of density-functional theory (DFT) is broadly considered the conceptual basis for a full characterization of an electronic system in its ground state by just the one-body particle density. In this Part~II of a…
The universal functional of Hohenberg-Kohn is given as a coupling-constant integral over the density as a functional of the potential. Conditions are derived under which potential-functional approximations are variational. Construction via…
In a recent PRL, Gonze et al claim that the density functional theory in Hohenberg-Kohn formulation is not valid for crystalline solids in a homogenious electric field. They introduce another theory, density-and-polarization functional…
Lieb's convex formulation of density-functional theory is presented in a pedagogical manner, emphasizing its connection to Hohenberg-Kohn theory and to Levy's constrained-search theory. The Hohenberg-Kohn and Lieb variation principles are…
In this work we establish a density-functional reformulation of coupled matter-photon problems subject to general external electromagnetic fields and charge currents. We first show that for static minimally-coupled matter-photon systems an…
It is considered constraints imposed by the quantum mechanics on the measurement of the density of the electromagnetic energy. First, the energy of the electromagnetic wave and the volume (time) are bound with the Heisenberg uncertainty…
An extended electron model fully recovers many of the experimental results of quantum mechanics while it avoids many of the pitfalls and remains generally free of paradoxes. The formulation of the many-body electronic problem here resembles…
The exact static and time-dependent Kohn-Sham (KS) exchange-correlation (xc) potential is extremely challenging to approximate as it is a local multiplicative potential that depends on the electron density everywhere in the system. The KS…
It is shown that, for isolated many-electron Coulomb systems with Coulombic external potentials, the usual reductio ad absurdum proof of the Hohenberg-Kohn theorem is unsatisfactory since the to-be-refuted assumption made about the…
A rigorous derivation of the density functional in the Hohenberg-Kohn theory is presented. With no assumption regarding the magnitude of the electric coupling constant $e^2$ (or correlation), this work provides a firm basis for…
The correlation holes for densities of equal and opposite spin around a test electron are determined from the Schr\"{o}dinger equation with proper boundary conditions. The traditional "exchange" term follows from the boundary condition…
The uniform electron gas placed between two reservoirs is used as a model system for molecular junctions under an external bias. The energetics of the electron gas are calculated by generalizing the Thomas-Fermi-Dirac (TFD) model to…
At the basis of much of computational chemistry is density functional theory, as initiated by the Hohenberg-Kohn theorem. The theorem states that, when nuclei are fixed, nuclear potentials are determined by $1$-electron densities. We recast…
The Hohenberg-Kohn theorem and the Kohn-Sham equations, which are at the basis of the Density Functional Theory, are reformulated in terms of a particular many-body density, which is translational invariant and therefore is relevant for…
The effects of the Ohmic and magnetic density currents are investigated in the linearized Euler-Heisenberg electrodynamics. The linearization is introduced through an external magnetic field, in which the vector potential of the…
Since Spin Density Functional Theory was first proposed, but also recently, examples were constructed to show that a spin-potential may share its ground state with other spin-potentials. In fact, for collinear magnetic fields and systems…
The Heisenberg uncertainty principle is one of the fundamental pillars of quantum mechanics and quantum field theory. It is normally introduced by postulating the commutation relations $[\hat{x}^i, \hat{p}^j] = i\hbar \delta^{ij}$. However,…
It is shown that in adiabatic approximation for nuclei the many-component Coulomb system cannot be described on the basis of the grand canonical ensemble. Using the variational Bogolyubov's procedure for the free energy, the Hohenberg-Kohn…
Hohenberg and Kohn have proven that the electronic energy and the one-particle electron density can, in principle, be obtained by minimizing an energy functional with respect to the density. While decades of theoretical work have produced…
We study the model of a noninteracting spinless electron gas confined to the two-dimensional localized surface of a cone in the presence of external magnetic fields. The localized region is characterized by an annular radial potential. We…