Related papers: Reconsidering Power Functional Theory
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
The aim of this paper is to establish density properties in $L^p$ spaces of the span of powers of functions $\{\psi^\lambda\,:\lambda\in\Lambda\}$, $\Lambda\subset\N$ in the spirit of the M\"untz-Sz\'asz Theorem. As density is almost never…
The paper is withdrawn due to an error in Section 2.
Following our previous work in [JCAP 1206, 041 (2012)], in this paper, we continue our study of reconstructing $f(R)$ modified gravity models that can be connected to a single scalar field in general relativity via conformal transformation,…
Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been…
The derivation of the state of the art tensorial versions of Fundamental Measure Theory (a form of classical Density Functional Theory for hard spheres) are re-examined in the light of the recently introduced concept of global stability of…
Density-functional theory is a formally exact description of a many-body quantum system in terms of its density; in practice, however, approximations to the universal density functional are required. In this work, a model based on deep…
Fractional analysis is applied to describe classical dynamical systems. Fractional derivative can be defined as a fractional power of derivative. The infinitesimal generators {H, .} and L=G(q,p) \partial_q+F(q,p) \partial_p, which are used…
In the present work we propose a theory for obtaining successively better approximations to the linear response functions of time-dependent density or current-density functional theory. The new technique is based on the variational approach…
This paper is devoted to the uniqueness problem of the power of a meromorphic function with its differential polynomial sharing a set. Our result will extend a number of results obtained in the theory of normal families. Some questions are…
Calculating perturbation response properties of materials from first principles provides a vital link between theory and experiment, but is bottlenecked by the high computational cost. Here a general framework is proposed to perform density…
Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values…
In the paper, we give partition-theoretic results for the coefficients of some mock theta functions and prove their congruence properties. Some recurrence relations connecting the coefficients of the mock theta functions with certain…
For the kinetic energy of 1d model finite systems the leading corrections to local approximations as a functional of the potential are derived using semiclassical methods. The corrections are simple, non-local functionals of the potential.…
Density functional theory (DFT) is an essential building block for modern theoretical physics, chemistry, and engineering, especially those concerning electronic properties. Through decades of development, various program packages for…
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula…
A generalization of the Density Functional Theory is proposed. The theory developed leads to single-particle equations of motion with a quasi-local mean-field operator, which contains a quasi-particle position-dependent effective mass and a…
The Baker-Campbell-Hausdorff formula was recently resummed exactly in one variable, and left as a power series in the other (Moodie and Long 2021 J. Phys. A: Math. Theor. 54 015208). The coefficients of the power series were provided as a…
The problem of extrapolating the series in powers of small variables to the region of large variables is addressed. Such a problem is typical of quantum theory and statistical physics. A method of extrapolation is developed based on…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…