Related papers: Differential Equation Approach for One- and Two- D…
In this work, we present a new result which concerns the derivation of the Green function relative to the time-independent Schrodinger equation in two dimensional space. The system considered in this work is a quantum particle that have an…
It is well known that second order linear ordinary differential equations with slowly varying coefficients admit slowly varying phase functions. This observation is the basis of the Liouville-Green method and many other techniques for the…
Given a spatially dependent mass we obtain the two-point Green's function for exactly solvable nonrelativistic problems. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger…
A linear singularly perturbed convection-diffusion problem with characteristic layers is considered in three dimensions. Sharp bounds for the associated Green's function and its derivatives are established in the $L_1$ norm. The dependence…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
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…
We construct the fundamental solution or Green function for a divergence form elliptic system in two dimensions with bounded and measurable coefficients. We consider the elliptic system in a Lipschitz domain with mixed boundary conditions.…
Learning the Green's function using deep learning models enables to solve different classes of partial differential equations. A practical limitation of using deep learning for the Green's function is the repeated computationally expensive…
In this paper, we build on the work of [T. Hughes, G. Sangalli, VARIATIONAL MULTISCALE ANALYSIS: THE FINE-SCALE GREENS' FUNCTION, PROJECTION, OPTIMIZATION, LOCALIZATION, AND STABILIZED METHODS, SIAM Journal of Numerical Analysis, 45(2),…
Motivated by the discovery of superconductivity in beta-pyrochlore oxides, we study property of rattling motion coupled with conduction electrons. We derive the general expression of the Green's function of fully anharmonic lattice…
In this paper, we present details of the dual fermion (DF) method to study the non-local correction to single site DMFT. The DMFT two-particle Green's function is calculated using continuous time quantum monte carlo (CT-QMC) method. The…
It is known that Green's functions can be expressed as continued fractions; the content at the $n$-th level of the fraction is encoded in a coefficient $b_n$, which can be recursively obtained using the Lanczos algorithm. We present a…
In this paper we develop a way of obtaining Green's functions for partial differential equations with linear involutions by reducing the equation to a higher-order PDE without involutions. The developed theory is applied to a model of heat…
We consider the free space Helmholtz Green's function and split it into the sum of oscillatory and non-oscillatory (singular) components. The goal is to separate the impact of the singularity of the real part at the origin from the…
A nonperturbative method to obtain on- and off-site one-particle Green's function is introduced and applied to noninteracting Hubbard model with next nearest neighbor hopping and interacting Hubbard model in large dimensions, for example.…
The pointwise space-time behavior of the Green's function of the three-dimensional relativistic Boltzmann equation is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive waves and…
We show that the Green's function of a two dimensional fermion with a modified dispersion relation and short distance parameter $a$ is given by the Lerch zeta function. The Green's function is defined on a cylinder of radius R and we show…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
Green's functions in Physics have proven to be a valuable tool for understanding fundamental concepts in different branches, such as electrodynamics, solid-state and many -body problems. In quantum mechanics advanced courses, Green's…
The problem of motion of a single electron interacting with a periodic lattice of two-level systems is investigated within a spinless fermion model. The Green's function is calculated in a single-site dynamical coherent potential…