Related papers: Scaling Invariance of Density Functionals
Finite temperature density functional theory provides, in principle, an exact description of the thermodynamical equilibrium of many-electron systems. In practical applications, however, the functionals must be approximated. Efficient and…
In a companion article we have introduced a notion of multiscale functional inequalities for functions $X(A)$ of an ergodic stationary random field $A$ on the ambient space $\mathbb R^d$. These inequalities are multiscale weighted versions…
The advent of the Hohenberg-Kohn theorem in 1964, its extension to finite-T, Kohn-Sham theory, and relativistic extensions provide the well-established formalism of density-functional theory (DFT). This theory enables the calculation of all…
A widely used approximation to the exchange-correlation functional in density functional theory is the local density approximation (LDA), typically derived from the properties of the homogeneous electron gas (HEG). We previously introduced…
In the context of functional data analysis, probability density functions as non-negative functions are characterized by specific properties of scale invariance and relative scale which enable to represent them with the unit integral…
We examine the equilibrium properties of hot, dilute, non-relativistic plasmas. The partition function and density correlation functions of a classical plasma with several species are expressed in terms of a functional integral over…
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,…
We develop an ensemble density functional theory for the fractional quantum Hall effect using a local density approximation. Model calculations for edge reconstructions of a spin-polarized quantum dot give results in good agreement with…
This paper extends the result of \cite{BM} on the homogenization of integral functionals with linear growth defined for Sobolev maps taking values in a given manifold. Through a $\Gamma$-convergence analysis, we identify the homogenized…
This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in…
Due to efficient scaling with electron number N, density functional theory (DFT) is widely used for studies of large molecules and solids. Restriction of an exact mean-field theory to local potential functions has recently been questioned.…
We study the electronic structure of a spherical jellium in the presence of a central Gaussian impurity. We test how well the resulting inhomogeneity effects beyond spherical jellium are reproduced by several approximations of density…
It is shown here that Kohn-Sham equations cannot be derived from Hohenberg-Kohn theory without an additional postulate. Assuming that a functional derivative with respect to total electron density exists leads in general to a theory…
We analyze a decomposition of the Coulomb electron-electron interaction into a long-range and a short-range part in the framework of density functional theory, deriving some scaling relations and the corresponding virial theorem. We study…
This book deals with functions allowing to express the dissimilarity (discrepancy) between two data fields or ''divergence functions'' with the aim of applications to linear inverse problems. Most of the divergences found in the litterature…
Inspired by earlier work on the band-gap problem in insulators, we reexamine the treatment of strongly correlated Hubbard-type models within density-functional theory. In contrast to previous studies, the density is fully parametrized by…
This article generalizes the notion of the local density of a many-body system to introduce collective coordinates as explicit degrees of freedom. It is shown that the energy of the system can be expressed as a functional of this object.…
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…
Energy functionals of the Green's function can simultaneously provide spectral and thermodynamic properties of interacting electrons' systems. Though powerful in principle, these formulations need to deal with dynamical…
A Lorentz invariant positive definite expression for photon number density is derived as the absolute square of the invariant scalar product of a polarization sensitive position eigenvector and the photon wave function. It is found that…