Related papers: On the Evaluation of the electron repulsion integr…
We consider four types of representations of solutions of GKZ system: series representations, Laplace integral representations, Euler integral representations, and Residue integral representations which will be introduced in this paper. In…
We describe algorithms to compute elliptic functions and their relatives (Jacobi theta functions, modular forms, elliptic integrals, and the arithmetic-geometric mean) numerically to arbitrary precision with rigorous error bounds for…
The univariate elliptic beta integral is represented as a bilinear combination of infinite $_{10}V_9$ very-well-poised elliptic hypergeometric series representing the sum of residues of the integrand poles. Convergence of this combination…
A numerical integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a…
A new algorithm to calculate Coulomb wave functions with all of its arguments complex is proposed. For that purpose, standard methods such as continued fractions and power/asymptotic series are combined with direct integrations of the…
This paper explores orbits in extended mass distributions and develops an analytic approximation scheme based on epicycloids (spirograph patterns). We focus on the Hernquist potential which provides a good model for many astrophysical…
In this paper, we propose an orbital iteration based parallel approach for electronic structure calculations. This approach is based on our understanding of the single-particle equations of independent particles that move in an effective…
Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of…
Based on the tensor method, a q-analoque of the spin-orbit coupling is introduced in a q-deformed Schroedinger equation, previously derived for a central potential. Analytic expressions for the matrix elemnets of the representation j=l\pm…
We point out that a typical two-electron distribution function in atoms and molecules often called the intracule depends sensitively on the electron-electron repulsion which leads to the so-called Coulomb correlation. The difference between…
The partition function of the Hubbard model with local attraction and long range Coulomb repulsion between electrons is written as a functional integral with an action $A$ involving a pairing field $\Delta$ and a local potential $V$. After…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
We analyze the full counting statistics of a multiorbital Kondo effect in a quantum dotwith the SU(N) symmetry in the framework of the renormalized perturbation theory. The current probability distribution function is calculated for an…
We present a robust strategy to numerically sample the Coulomb potential in reciprocal space for periodic Born-von Karman cells of general shape. Our approach tackles two common issues of plane-wave based implementations of Coulomb…
Seeking for a relativistic generalisation of the non-relativistic Schroedinger equation, one very soon arrives at equations with a square-root operator by having applied the quantum mechanical correspondence principle to the formula of…
Recursion relations for Hylleraas three-electron integral are obtained in a closed form by using integration by parts identities. Numerically fast and well stable algorithm for the calculation of the integral with high powers of…
We calculate in a linear response the admittance of a quantum dot out of equilibrium. The interaction between two electrons with opposite spins simultaneously residing on the resonant level is modeled by an Anderson Hamiltonian. The…
We study two classes of radial integrals involving a product of bound and continuum one-electron states. Using a representation of the continuum part with an expansion on complex Gaussian Type Orbitals, such integrals can be performed…
The differential and partially integrated cross sections are considered for bremsstrahlung from high-energy electrons in atomic field with the exact account of this field. The consideration exploits the quasiclassical electron Green's…