Related papers: Studies on optimizing potential energy functions f…
We first study subextensions of m-subharmonic functions in weighted energy classes with given boundary values. The results are used to approximate an m-subharmonic function in weighted energy classes with given boundary values by an…
We study the classical problem of characterizing the channel capacity and its achieving distribution in a generic fashion. We derive a simple relation between three parameters: the input-output function, the input cost function and the…
In this paper, we introduce methods from convex optimization to solve the multimarginal transport type problems arise in the context of density functional theory. Convex relaxations are used to provide outer approximation to the set of…
In the framework of zeta-function approach the Casimir energy for three simple model system: single delta potential, step function potential and three delta potentials is analyzed. It is shown that the energy contains contributions which…
We use the theory of rectifiable metric spaces to define a Dirichlet energy of Lipschitz functions defined on the support of integral currents. This energy is obtained by integration of the square of the norm of the tangential derivative,…
The optimized effective potential (OEP) approach has so far mainly been used in benchmark studies and for the evaluation of band gaps. In this work, we extend the application of the OEP by determining the analytical ionic forces within the…
The analytic theory presented in Paper I is converted into a form convenient for numerical analysis. A fast and accurate code has been written using this numerical formulation. The results are presented by first defining a reference set of…
$\newcommand{\EC}{\mathsf{EC}}\newcommand{\KW}{\mathsf{KW}}\newcommand{\DT}{\mathsf{DT}}\newcommand{\psens}{\mathsf{psens}} \newcommand{\calB}{{\cal B}} $ For a Boolean function $f:\{0,1\}^n \to \{0,1\}$ computed by a circuit $C$ over a…
We summarize several semi-phenomenological approaches to estimate the internal energy of one-component-plasma (OCP) in two (2D) and three (3D) dimensions. Particular attention is given to a hybrid approach, which reproduces the…
The calculation of the effective potential for fixed-end and toroidal rigid $p$-branes is performed in the one-loop as well as in the $1/d$ approximations. The analysis of the involved zeta-functions (of inhomogeneous Epstein type) which…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
We discuss two aspects of the color dipole picture of high energy photon-proton scattering. First we present bounds on various ratios of deep inelastic structure functions resulting from the dipole picture that, together with the measured…
We obtain an analytic solution for a three-parameter class of logarithmic potentials at zero energy. The potential terms are products of the inverse square and the inverse log to powers 2, 1 and 0. The configuration space is the…
We have studied the structure and properties of potassium clusters containing even number of atoms ranging from 2 to 20 at the ab initio level. The geometry optimization calculations are performed using all-electron density functional…
In this paper, we obtain results about the positive definiteness, the continuity and the level-boundedness of two optimal value functions of specific parametric optimization problems. Those two optimization problems are generalizations of…
Three-point semidefinite programming bounds are one of the most powerful known tools for bounding the size of spherical codes. In this paper, we use them to prove lower bounds for the potential energy of particles interacting via a pair…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
We use frequency-dependent capacitance-voltage spectroscopy to measure the tunneling probability into self-assembled InAs quantum dots. Using an in-plane magnetic field of variable strength and orientation, we are able to obtain information…
We study 2-point and 3-point functions in CFT at finite temperature for large dimension operators using holography. The 2-point function leads to a universal formula for the holographic free energy in $d$ dimensions in terms of the…