Related papers: On the Evaluation of the electron repulsion integr…
The cumulant expansion is a powerful approach for including correlation effects in electronic structure calculations beyond the GW approximation. However, current implementations are incomplete since they ignore terms that lead to partial…
Gausslets are one of the few basis constructions for electronic structure that combine locality, orthonormality, variable resolution, and an accurate diagonal approximation for the electron-electron interaction, but the original…
The electron-electron mutual Coulomb repulsion energy density functional satisfies an equation that links functionals and functional derivatives at N-electron and (N-1)-electron densities for densities determined from the same adiabatic…
Calculations of the ground state of inhomogeneous many-electron systems involve a solving of the Poisson equation for Coulomb potential and the Schroedinger equation for single-particle orbitals. Due to nonlinearity and complexity this set…
Highest-weight representations of infinite dimensional Lie algebras and Hilbert schemes of points are considered, together with the applications of these concepts to partition functions, which are most useful in physics. Partition functions…
Wavefunctions for large electron numbers suffer from an exponential growth of the Hilbert space which is required for their description. In fact, as pointed out by W. Kohn, for electron numbers $N > N_0$ where $N_0 \approx 10^3$ they become…
Hypergeometric structures in single and multiscale Feynman integrals emerge in a wide class of topologies. Using integration-by-parts relations, associated master or scalar integrals have to be calculated. For this purpose it appears useful…
Parametric Feynman integrals with the regions of integration defined by some polynomials are considered in this paper. It is shown that integrals with irregular integration regions can be converted to standard parametric integrals, for…
A Kepler solver is an analytical method used to solve a two-body problem. In this paper, we propose a new correction method by slightly modifying the Kepler solver. The only change to the analytical solutions is that the obtainment of the…
A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…
The conditions for superintegrable systems in two-dimensional Euclidean space admitting separation of variables in an orthogonal coordinate system and a functionally independent third-order integral are studied. It is shown that only…
This paper derives and demonstrates a new, purely density-based ab initio approach for calculation of the energies and properties of many-electron systems. It is based upon the discovery of relationships that govern the "mechanics" of the…
Approximate bound state solutions of the spinless Salpeter equation for the Hellmann potential are studied for heavy particles. By using functional analysis method, an analytical expression for the energy levels, and the corresponding…
The indefinite integral $$ \int x^\alpha e^{\eta x^\beta}\,_pF_q (a_1, a_2, \cdot\cdot\cdot a_p; b_1, b_2, \cdot\cdot\cdot, b_q; \lambda x^{\gamma})dx, $$ where $\alpha, \eta, \beta, \lambda, \gamma\ne0$ are real or complex constants and…
The coadjoint orbits for the series $B_l,\ C_l$ and $D_l$ are considered in the case when the base point is a multiple of a fundamental weight. A quantization of the big cell is suggested by means of introducing a $\ast$-algebra generated…
The spinless relativistic Coulomb problem is the bound-state problem for the spinless Salpeter equation (a standard approximation to the Bethe--Salpeter formalism as well as the most simple generalization of the nonrelativistic…
As a generalization of Riemann-Liouville integral, we introduce integral transformations of convergent power series which can be applied to hypergeometric functions with several variables.
The formalism developed in Refs.~\cite{Guo:2023ecc,Guo:2024zal,Guo:2024pvt} that relates the integrated correlation functions for a trapped system to the infinite volume scattering phase shifts through a weighted integral is further…
We report on our analysis of the Coulomb singularity problem in the frame of the coupled channel scattering theory including spin-orbit interaction. We assume that the coupling between the partial wave components involves orbital angular…
We study numerically the geometric entanglement in the Laughlin wave function, which is of great importance in condensed matter physics. The Slater determinant having the largest overlap with the Laughlin wave function is constructed by an…