Related papers: Scaling Invariance of Density Functionals
We investigate ergodic-theoretical quantities and large deviation properties of one-dimensional intermittent maps, that have not only an indifferent fixed point but also a singular structure such that the uniform measure is invariant under…
The present paper deals with the asymptotic behavior of equi-coercive sequences $\{\mathcal{F}_n\}$ of nonlinear functionals defined over vector-valued functions in $W_)^{1,p}(\Omega)^M$ , where $p>1$, $M\ge1$, and $\Omega$ is a bounded…
We introduce a Lagrangian density for M-Theory which is purely topological using Gelfand-Fuchs cohomology. Next we calculate the partition function which indeed gives topological invariants that can be expressed via the Ray-Singer analytic…
A unified formulation of the density functional theory is constructed on the foundations of entropic inference in both the classical and the quantum regimes. The theory is introduced as an application of entropic inference for inhomogeneous…
Density functional theory is currently the most widely applied method in electronic structure theory. The Kohn-Sham method, based on a fictitious system of non-interacting particles, is the work horse of the theory. The particular form of…
Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…
Understanding the properties of warm dense hydrogen is of key importance for the modeling of compact astrophysical objects and to understand and further optimize inertial confinement fusion (ICF) applications. The work horse of warm dense…
The aim of this paper is to establish density properties in $L^p$ spaces of the span of powers of functions $\{\psi^\lambda\,:\lambda\in\Lambda\}$, $\Lambda\subset\N$ in the spirit of the M\"untz-Sz\'asz Theorem. As density is almost never…
Density functional theory is generalized to incorporate electron-phonon coupling. A Kohn-Sham equation yielding the electronic density $n_U(\mathbf{r})$, a conditional probability density depending parametrically on the phonon normal mode…
The principles of density-functional theory are studied for finite lattice systems represented by graphs. Surprisingly, the fundamental Hohenberg-Kohn theorem is found void in general, while many insights into the topological structure of…
Let f_n denote a kernel density estimator of a continuous density f in d dimensions, bounded and positive. Let \Psi(t) be a positive continuous function such that \|\Psi f^{\beta}\|_{\infty}<\infty for some 0<\beta<1/2. Under natural…
Recently, Tao and Mo (TM) derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the…
Starting from a general classical model of many interacting particles we present a well defined step by step procedure to derive the continuum-mechanics equations of nonlinear elasticity theory with fluctuations which describe the…
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
We consider iterated function systems (IFS) in ${\mathbb R}^d$ for $d\ge 3$ of the form $\{f_j(x) = \lambda {\mathcal O} x + a_j\}_{j=0}^m$, with $a_0=0$ and $m\ge 1$. Here $\lambda\in (0,1)$ is the contraction ratio and ${\mathcal O}$ is…
A stochastic minimization method for a real-space wavefunction, $\Psi({\bf r}_{1},{\bf r}_{2}\ldots{\bf r}_{n})$, constrained to a chosen density, $\rho({\bf r})$, is developed. It enables the explicit calculation of the Levy constrained…
In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Ideal density-functional approximations (DFAs) should account for dynamic, static, and nondynamic correlation. While common DFAs struggle with the latter two, the Ziegler-Rauk-Baerends-Daul multiplet sum method (MSM) provides a pragmatic…
Fractional occupation numbers can be used in density functional theory to create a symmetric Kohn-Sham potential, resulting in orbitals with degenerate eigenvalues. We develop the corresponding perturbation theory and apply it to a system…