相关论文: Some Square Lattice Green Function Formulas
We derive formulas for the matrix elements of the lattice Green function for the discrete Poisson equation on an infinite square lattice. The partial difference equation for the matrix elements is solved by reducing it to a series of first…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…
In this Brief Report, we present an algorithm for calculating the elastic Lattice Greens Function of a regular lattice, in which defects are created by removing lattice points. The method is computationally efficient, since the required…
It is shown that the Green's function on a finite lattice in arbitrary space dimension can be obtained from that of an infinite lattice by means of translation operator. Explicit examples are given for one- and two-dimensional lattices.
Lattice Green functions appear in lattice gauge theories, in lattice models of statistical physics and in random walks. Here, space coordinates are treated as parameters and series expansions in the mass are obtained. The singular points in…
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…
A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…
Efficient computation of lattice defect geometries such as point defects, dislocations, disconnections, grain boundaries, interfaces and free surfaces requires accurate coupling of displacements near the defect to the long-range elastic…
We obtain simple formulas for the matrix elements of the resolvent operator (the Green's function) in any finite set of square integrable basis. These formulas are suitable for numerical computations whether the basis elements are…
In this note we present the Green's functions and density of states for the most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, and Lieb lattice. Though the results are well know, we hope that their derivation…
Multipole matrix elements of Green function of Laplace equation are calculated. The multipole matrix elements of Green function in electrostatics describe potential on a sphere which is produced by a charge distributed on the surface of a…
We show how to use the lattice Green function to calculate capacitances in two dimensions with boundary conditions at infinity. It is shown how to calculate coefficients of capacitance and induction from the lattice Green function. A…
We write the Green function of the $d$-dimensional hypercubic lattice in a piecewise form covering the entire real frequency axis. Each piece is a single integral involving modified Bessel functions of the first and second kinds. The…
A matrix basis formulation is introduced to represent the 3 x 3 dyadic Green's functions in the frequency domain for the Maxwell's equations and the elastic wave equation in layered media. The formulation can be used to decompose the…
An expression for the Green's function (GF) of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are…
A explicit formula on semiclassical Green functions in mixed position and momentum spaces is given, which is based on Maslov's multi-dimensional semiclassical theory. The general formula includes both coordinate and momentum representations…
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…
We previously reported on a recursive method to generate the expansion of the lattice Green function of the $d$-dimensional face-centred cubic lattice (fcc). The method was used to generate many coefficients for d=7 and the corresponding…
Asymptotic formulae for Green's functions for the operator $-\GD$ in domains with small holes are obtained. A new feature of these formulae is their uniformity with respect to the independent variables. The cases of multi-dimensional and…
1D lattice summations of the 3D Green's function are needed in many applications such as photonic crystals, antenna arrays, and so on. Such summations are usually divided into two cases, depending on the location of the observer: Out of the…