Related papers: Multipole matrix elements of Green function of Lap…
We obtain the two-point Green's function for the relativistic Dirac-Oscillator problem. This is accomplished by setting up the relativistic problem in such a way that makes comparison with the nonrelativistic problem highly transparent and…
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…
The Laplace equation in three dimensional Euclidean space is $R$-separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lam\'e-Wangerin functions called internal and external bi-cyclide harmonics. An…
We propose a framework to construct the ground-state energy and density matrix of an N-electron system by solving selfconsistently a set of single-particle equations. The method can be viewed as a non-trivial extension of the Kohn-Sham…
An efficient surface integral equation-based method is proposed for the analysis of electromagnetic scattering from multilayered media containing complex periodic inclusions. The proposed method defines equivalent currents at the interfaces…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
Based on the Korringa-Kohn-Rostoker Green's function technique we present a computational scheme for calculating the electronic structure of layered systems with homogeneous spin-spiral magnetic state. From the self-consistent…
In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on…
We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based…
The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and…
We quantize the Maxwell theory in the presence of a electric charge in a "dual" Loop Representation, i.e. a geometric representation of magnetic Faraday's lines. It is found that the theory can be seen as a theory without sources, except by…
In this paper, we present a quantum computational method to calculate the many-body Green's function matrix in a spin orbital basis. We apply our approach to finite-sized fermionic Hubbard models and related impurity models within Dynamical…
The Fast Multipole Method (FMM) obeys periodic boundary conditions "natively" if it uses a periodic Green function for computing the multipole expansion in the interaction zone of each FMM oct-tree node. One can define the "optimal" Green…
Several photoemission spectroscopies and, in particular, Auger spectroscopy, involve double-ionization processes. For the numerical simulation of these spectroscopies it is convenient to use the particle-particle channel of the two-body…
The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and…
This paper uses the convolution theorem of the Laplace transform to derive new inverse Laplace transforms for the product of two parabolic cylinder functions in which the arguments may have opposite sign. These transforms are subsequently…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
We propose an efficient algorithm for the evaluation of the potential and its gradient of gravitational/electrostatic $N$-body systems, which we call particle mesh multipole method (PMMM or PM$^3$). PMMM can be understood both as an…
In this research paper, we present an exact matrix form analytical solution of the multi-dimensional generalized Langevin equation with quadratic potentials. Our investigation provides detailed expressions for the two-dimensional…
Across many areas of physics, multipole expansions are used to simplify problems, solve differential equations, calculate integrals, and process experimental data. Spherical harmonics are the commonly used basis functions for a multipole…