Related papers: Reconsidering Power Functional Theory

We simplify the proof of some widely used theoretical theorems, extending their applicability, while correcting some erroneous results. We also generalize key results and present new results that contribute to the development of the theory.…

In this survey we discuss derivatives of the Wright functions (of the first and the second kind) with respect to parameters. Differentiation of these functions leads to infinite power series with coefficient being quotients of the digamma…

Time-dependent density functional theory has emerged as a method of choice for calculations of spectra and response properties in physics, chemistry, and biology, with its system-size scaling enabling computations on systems much larger…

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…

Jeffery's 1861 computations using finite difference calculus are resurrected and extended from forward differences to general delta operators and used to neatly prove theorems in the Rota--Mullins theory of polynomials of binomial type…

We explore a variety of unsolved problems in density functional theory, where mathematicians might prove useful. We give the background and context of the different problems, and why progress toward resolving them would help those doing…

We review the progress that has been recently made in the application of time-dependent density functional theory to thermoelectric phenomena. As the field is very young, we emphasize open problems and fundamental issues. We begin by…

Density functional theory for a simple model of dendrimers is proposed. The theory is based on fundamental measure theory which accounts for the hard-sphere repulsion of the segments and on the Wertheim first-order perturbation theory for…

Power systems are undergoing unprecedented transformations with the incorporation of larger amounts of renewable energy sources, distributed generation and demand response. All these changes, while potentially making power grids more…

The excess free energy functional of classical density functional theory depends upon the type of fluid model, specifically on the choice of (pair) potential, is unknown in general, and is approximated reliably only in special cases. We…

The famous equivalence theorem is reexamined in order to make it applicable to the case of intrinsically quantum infinite-component effective theories. We slightly modify the formulation of this theorem and prove it basing on the notion of…

We discuss the relationship between modern time-dependent density functional theory and earlier time-periodic versions, and why the criticisms in a recent paper (Chem. Phys. Lett. {\bf 433} (2006) 204) of our earlier analysis (Chem. Phys.…

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…

Using elementary methods we find surprising connections between the values of the Riemann Zeta Function over integers and the fractional parts of rational powers, and a connection between the Riemann Zeta Function and the Prime Zeta…

We address a deep study of the convexity notions that arise in the study of weak* lower semicontinuity of supremal functionals as well as those raised by the power-law approximation of such functionals. Our quest is motivated by the…

Forty-five years after the point de d\'epart [1] of density functional theory, its applications in chemistry and the study of electronic structures keep steadily growing. However, the precise form of the energy functional in terms of the…

In a paper recently published in Phys. Rev. A [arXiv:1010.4223], Schirmer has criticized an earlier work of mine [arXiv:0803.2727], as well as the foundations of time-dependent density functional theory. In Ref.[2], I showed that the…

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

The effective action for the charge density and the photon field is proposed as a generalization of the density functional. A simple definition is given for the density functional, as the functional Legendre transform of the generator…

We derive properties of powers of a function satisfying a second-order linear differential equation. In particular we prove that the n-th power of the function satisfies an (n+1)-th order differential equation and give a simple method for…