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The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…
Macroscopic field quantization is presented for a nondispersive photonic dielectric environment, both in the absence and presence of guest atoms. Starting with a minimal-coupling Lagrangian, a careful look at functional derivatives shows…
We calculate the energy spectrum of an electron moving in a two-dimensional lattice which is defined by an electric potential and an applied perpendicular magnetic field modulated by a periodic surface magnetization. The spatial direction…
We propose an algorithm for the application of the Laplace method for the calculation of the simplest Feynman diagram with a single loop in the scalar {\phi}^3 theory. The calculation of the contribution of such a diagram to the scattering…
The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic…
The modified Poisson-Boltzmann (MPB) equations are often used to describe equilibrium particle distribution of ionic systems. In this paper, we propose a fast algorithm to solve MPB equations with the self Green's function as the self…
This article is devoted to deduce the expression of the Green's function related to a general constant coefficients fractional difference equation coupled to Dirichlet conditions. In this case, due to the points where some of the fractional…
The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational…
Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of $N$ scatterers. Wave-functions are expanded in a spherical-wave basis on…
On the basis of the tight-binding formalism and Green function technique we obtain all the Green functions matrix elements for a biased chain with a linear variation of the electron on-site energy. Their dependence on the system parameters…
A revised new iterative method based on Green function defined by quadratures along a single trajectory is developed and applied to solve the ground state of the double-well potential. The result is compared to the one based on the original…
Many-body Green's functions encode all the properties and excitations of interacting electrons. While these are challenging to be evaluated accurately on a classical computer, recent efforts have been directed towards finding quantum…
We perform a bivariate Taylor expansion of the axisymmetric Green function in order to determine the exterior potential of a static thin toroidal shell having a circular section, as given by the Laplace equation. This expansion, performed…
We introduce a fast algorithm for computing volume potentials - that is, the convolution of a translation invariant, free-space Green's function with a compactly supported source distribution defined on a uniform grid. The algorithm relies…
We present and analyze results of the relativistic coupled-cluster calculation of energies, hyperfine constants, and dipole matrix elements for the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states of Li atom. The calculations are complete through…
We present a generalization of the maximum entropy method to the analytic continuation of matrix-valued Green's functions. To treat off-diagonal elements correctly based on Bayesian probability theory, the entropy term has to be extended…
We propose a method to calculate the Greens function of a free massive scalar field on the lattice numerically to very high precision. For masses m < 2 (in lattice units) the massive Greens function can be expressed recursively in terms of…
This manuscript introduces a generalization of the Mellin integral transform within the framework of weighted fractional calculus with respect to an increasing function. The proposed transform is much more suitable for working with…
The Laplace-Beltrami problem $\Delta_\Gamma \psi = f$ has several applications in mathematical physics, differential geometry, machine learning, and topology. In this work, we present novel second-kind integral equations for its solution…
We establish existence and pointwise estimates of fundamental solutions and Green's matrices for divergence form, second order strongly elliptic systems in a domain $\Omega \subseteq \mathbb{R}^n$, $n \geq 3$, under the assumption that…