Related papers: Relationship between H\"{o}lder Divergence and Fun…

Standard approximations for the exchange-correlation (XC) functional in Kohn-Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly-correlated electronic systems. Partition-DFT (PDFT) is…

Gross-Oliveira-Kohn density-functional theory (GOK-DFT) is an extension of DFT to excited states where the basic variable is the ensemble density, i.e. the weighted sum of ground- and excited-state densities. The ensemble energy (i.e. the…

In this paper we are interested in testing whether there are any signals hidden in high dimensional noise data. Therefore we study the family of goodness-of-fit tests based on $\Phi$-divergences including the test of Berk and Jones as well…

Solving the fundamental and optical gap problems, which yield information about charged and neutral excitations in electronic systems, is one of the biggest challenge in density-functional theory (DFT). Despite their intrinsic difference,…

We establish an inequality which involves a non-negative function defined on the vertices of a finite $m$-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree…

Aspects of Density Functional Resonance Theory (DFRT) [Phys. Rev. Lett. \textbf{107}, 163002 (2011)], a recently developed complex-scaled version of ground-state Density Functional Theory (DFT), are studied in detail. The asymptotic…

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…

We introduce the semiclassical limit to electronic systems by taking the limit $\hbar\rightarrow 0$ in the solution of Schr\"odinger equations. We show that this limit is closely related to one type of strong correlation that is…

The original derivation of Power Functional Theory, Schmidt and Brader, JCP 138, 214101 (2013), is reworked in some detail with a view to clarifying and simplifying the logic and making explicit the various functional dependencies. We note…

Dimensions of level sets of generic continuous functions and generic H\"older functions defined on a fractal $F$ encode information about the geometry, ``the thickness" of $F$. While in the continuous case this quantity is related to a…

At the present time reliably established that probability density functions of gene expression of microarray experiments possess a number of universal properties. First of all these distributions have power asymptotic and secondly the shape…

We present a generalization of the Li, Nunes and Vanderbilt density-matrix method to the case of a non-orthogonal set of basis functions. A representation of the real-space density matrix is chosen in such a way that only the overlap…

We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…

Starting from a microscopic particle model whose hydrodynamic limit under hyperbolic space-time scaling is a 1D conservation law, we derive the large deviation rate function encoding the probability to observe a density profile which is a…

We investigate a density-functional theory (DFT) approach for an unpolarized trapped dilute Fermi gas in the unitary limit . A reformulation of the recent work of T. Papenbrock [Phys. Rev. A, {\bf 72}, 041602(R) (2005)] in the language of…

Density functional theory stems from the Hohenberg-Kohn-Sham-Mermin (HKSM) theorem in the grand canonical ensemble (GCE). However, as recent work shows, although its extension to the canonical ensemble (CE) is not straightforward, work in…

Let $\mathcal{F}\subseteq \binom{[n]}{r}$ be an intersecting family of sets and let $\Delta(\mathcal{F})$ be the maximum degree in $\mathcal{F}$, i.e., the maximum number of edges of $\mathcal{F}$ containing a fixed vertex. The…

We revisit the equilibrium statistical mechanics of a classical fluid of point-like particles with repulsive power-law pair interactions, focusing on density and energy fluctuations at finite temperature. Such long-range interactions,…

Classical density functional theory (DFT) provides an exact variational framework for determining the equilibrium properties of inhomogeneous fluids. We report a generalization of DFT to treat the non-equilibrium dynamics of classical…

We propose a systematic and constructive way to determine the exchange-correlation potentials of density-functional theories including vector potentials. The approach does not rely on energy or action functionals. Instead it is based on…