Related papers: Coordinates, modes and maps for the density functi…
Partition density functional theory is a formally exact procedure for calculating molecular properties from Kohn-Sham calculations on isolated fragments, interacting via a global partition potential that is a functional of the fragment…
We extend the density functional perturbation theory formalism to the case of non-collinear magnetism. The main problem comes with the exchange-correlation (XC) potential derivatives, which are the only ones that are affected by the…
In a homogeneous medium, the far-field generated by a localized source can be expanded in terms of multipoles; the coefficients are determined by the moments of the localized charge distribution. We show that this structure survives to some…
Stochastic spectral methods are efficient techniques for uncertainty quantification. Recently they have shown excellent performance in the statistical analysis of integrated circuits. In stochastic spectral methods, one needs to determine a…
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…
We develop convergent variational perturbation theory for quantum statistical density matrices. The theory is applicable to polynomial as well as nonpolynomial interactions. Illustrating the power of the theory, we calculate the…
We give formulas for the density of the measure of orthogonality for orthonormal polynomials with unbounded recurrence coefficients. The formulas involve limits of appropriately scaled Tur\'an determinants or Christoffel functions. Exact…
In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
In the framework of the Density Functional Theory for superconductors, we study the restoration of the particle number symmetry by means of the projection technique. Conceptual problems are outlined and numerical difficulties are discussed.…
We analyse a path to construct density functionals for the dispersion interaction energy from an expression in terms of the ground state densities and exchange-correlation holes of the isolated fragments. The expression is based on a…
This article is concerned with the mathematical analysis of the perturbation method for extended Kohn-Sham models, in which fractional occupation numbers are allowed. All our results are established in the framework of the reduced…
We use density-functional methods to study the effects of an external magnetic field on two-dimensional quantum dots with a rectangular hard-wall confining potential. The increasing magnetic field leads to spin polarization and formation of…
We present a simple formalism for the calculation of the derivatives of the electronic density matrix at any order, within density functional theory. Our approach, contrary to previous ones, is not based on the perturbative expansion of the…
Many high-dimensional uncertainty quantification problems are solved by polynomial dimensional decomposition (PDD), which represents Fourier-like series expansion in terms of random orthonormal polynomials with increasing dimensions. This…
Fractional occupation numbers can produce open-shell degeneracy in density functional theory. We develop the corresponding perturbation theory by requiring that a differentiable map connects the initial and perturbed states. The degenerate…
The macroscopic properties of a quantum system strongly depend on the spreading of the physical eigenfunctions (wavefunctions) of its Hamiltonian operador over its confined domain. The wavefunctions are often controlled by classical or…
A hypergeometric type equation satisfying certain conditions defines either a finite or an infinite system of orthogonal polynomials. We present in a unified and explicit way all these systems of orthogonal polynomials, the associated…
Hexagon relations are combinatorial or algebraic realizations of four-dimensional Pachner moves. We introduce some simple set-theoretic hexagon relations and then `quantize' them using what we call `polynomial hexagon cohomologies'. Based…
Inspired by the works in [1] and [8] we introduce what we call $k$-th-order fluctuation fields and study their scaling limits. This construction is done in the context of particle systems with the property of orthogonal self-duality. This…