Related papers: A remark on the local density approximation with t…

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…

We prove a novel result wherein the density function of the gradients---corresponding to density function of the derivatives in one dimension---of a thrice differentiable function S (obtained via a random variable transformation of a…

We obtain correction terms to the large N asymptotic expansions of the eigenvalue density for the Gaussian unitary and Laguerre unitary ensembles of random N by N matrices, both in the bulk of the spectrum and near the spectral edge. This…

We have adapted the maximally-localized Wannier function approach of [I. Souza, N. Marzari and D. Vanderbilt, Phys. Rev. B 65, 035109 (2002)] to the density functional theory based Siesta method [J. M. Soler et al., J. Phys.: Cond. Mat. 14,…

The study of defects in materials is of utmost importance for technological applications and the design of new materials. In this work, we analyze the performance of density functional approximations on two prototypical sets of defective…

Time dependent quantum systems are the subject of intense inquiry, in mathematics, science, and engineering, particularly at the atomic and molecular levels. In 1984, Runge and Gross introduced time dependent density functional theory…

We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…

For the problem of molecular solvation, formulated as a liquid submitted to the external potential field created by a molecular solute of arbitrary shape dissolved in that solvent, we draw a connection between the Gaussian field theory…

In density functional theory, simpler exchange-correlation (XC) approximations such as the local density approximation (LDA) are favored for computational speed but rely on limited information, leading to a trade-off between accuracy and…

Let $Q$ be a nonempty closed and convex subset of a real Hilbert space $% \mathcal{H}$, $S:Q\rightarrow Q$ a nonexpansive mapping, $A:Q\rightarrow Q$ an inverse strongly monotone operator, and $f:Q\rightarrow Q$ a contraction mapping. We…

For a twice continuously differentiable function $S$, we define the density function of its gradient (derivative in one dimension) $s = S^{\prime}$ as a random variable transformation of a uniformly distributed random variable using $s$ as…

The construction of non-empirical density functional approximations is typically guided by the satisfaction of exact constraints. An important constraint is the recovery of the gradient expansion for slowly varying electron densities. In…

Graph-based approximation methods are of growing interest in many areas, including transportation, biological and chemical networks, financial models, image processing, network flows, and more. In these applications, often a basis for the…

The approximation of smooth functions with a spectral basis typically leads to rapidly decaying coefficients where the rate of decay depends on the smoothness of the function and vice-versa. The optimal number of degrees of freedom in the…

The spectral density of random graphs with topological constraints is analysed using the replica method. We consider graph ensembles featuring generalised degree-degree correlations, as well as those with a community structure. In each case…

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…

Variable kernel density estimation allows the approximation of a probability density by the mean of differently stretched and rotated kernels centered at given sampling points $y_n\in\mathbb{R}^d,\ n=1,\dots,N$. Up to now, the choice of the…

Let $G$ be a connected reductive group acting on a complex vector space $V$ and projective space ${\mathbb P}V$. Let $x\in V$ and ${\cal H}\subseteq {\cal G}$ be the Lie algebra of its stabilizer. Our objective is to understand points…

In high-contrast composite materials, the electric field concentration is a common phenomenon when two inclusions are close to touch. It is important from an engineering point of view to study the dependence of the electric field on the…

A new implementation is proposed for including van der Waals interactions in Density Functional Theory using the Maximally-Localized Wannier functions. With respect to the previous DFT/vdW-WF method, the present DFT/vdW-WF2 approach, which…