相关论文: Coordinates, modes and maps for the density functi…
A remarkable consequence of the Hohenberg-Kohn theorem of density functional theory is the existence of an injective map between the electronic density and any observable of the many electron problem in an external potential. In this work,…
Properties of steady compressible flow for which geometric constraints have been placed on the potential function are derived, under hypotheses on the flow density and the singular set. Some related unconstrained problems are also…
A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and…
Time and spatial damping of transverse magnetohydrodynamic (MHD) kink oscillations is a source of information on the cross-field variation of the plasma density in coronal waveguides. We show that a probabilistic approach to the problem of…
We present a scheme for investigating arbitrary thermal observables in spatially inhomogeneous equilibrium many-body systems. Extending the grand canonical ensemble yields any given observable as an explicit hyper-density functional.…
Orthogonal polynomials for the multivariate hypergeometric distribution are defined on lattices in polyhedral domains in $\RR^d$. Their structures are studied through a detailed analysis of classical Hahn polynomials with negative integer…
The Kohn-Sham scheme of density functional theory is one of the most widely used methods to solve electronic structure problems for a vast variety of atomistic systems across different scientific fields. While the method is fast relative to…
We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition…
Perturbative expansions in physical applications are generically divergent, and their physical content can be studied using Borel analysis. Given just a finite number of terms of such an expansion, this input data can be analyzed in…
The density of polynomials in a weighted space of infinitely differentiable functions in a multidimensional real space is proved under minimal conditions on weight functions and on differences between weight functions. We apply this result…
Resonances of the (Frobenius-Perron) evolution operator P for phase-space densities have recently attracted considerable attention, in the context of interrelations between classical and quantum dynamics. We determine these resonances as…
New extra series of conserved densities for the polytropic gas model and nonlinear elasticity equation are obtained without any references to the recursion operator or to the Lax operator formalism. Our method based on the utilization of…
Force fields are usually formulated directly in nuclear configuration space, whereas density functional theory is naturally formulated in terms of external potentials, densities, and variational duality. We show that exact force fields are…
Large scale density modes are difficult to measure because they are sensitive to systematic observational errors in galaxy surveys, but we can study them indirectly by observing their impact on small scale perturbations. Cosmological…
The Hankel determinant representations for the partition function and boundary correlation functions of the six-vertex model with domain wall boundary conditions are investigated by the methods of orthogonal polynomial theory. For specific…
We write spectral decomposition of the hypergeometric differential operator on the contour $Re z=1/2$ (multiplicity of spectrum is 2). As a result, we obtain an integral transform that differs from the Jacobi (or Olevsky) transform. We also…
A detailed convex analysis-based formulation of density-functional theory for periodic systems in arbitrary dimensions is presented. The electron-electron interaction is taken to be of Yukawa type, harmonising with underlying function…
Let $d\nu$ be a measure in $\mathbb{R}^d$ obtained from adding a set of mass points to another measure $d\mu$. Orthogonal polynomials in several variables associated with $d\nu$ can be explicitly expressed in terms of orthogonal polynomials…
Resonances of the time evolution (Frobenius-Perron) operator P for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical and quantum dynamics. Efficient methods to determine…
We construct explicit easily implementable polynomial approximations of sufficiently high accuracy for locally constant functions on the union of disjoint segments. This problem has important applications in several areas of numerical…