Related papers: The Green's function of a finite-gap Schr\"odinger…
We study Schr\"odinger operators on compact finite metric graphs subject to $\delta$-coupling and standard boundary conditions. We compare the $n$-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the…
We prove essential self-adjointness for a semibounded from below discrete magnetic Schr\"{o}dinger operator in a space that represents a combinatorial model of the two-dimensional Euclidean space. The Dezin discretization scheme is used for…
We consider the problem of discretizing one-dimensional, real-valued functions as graphs. The goal is to find a small set of points, from which we can approximate the remaining function values. The method for approximating the unknown…
The finite difference time domain (FDTD) algorithm and Green function algorithm are implemented into the numerical simulation of electromagnetic scattering by ordinary objects in Schwarzschild space-time. FDTD method in curved space-time is…
The electromagnetic Green's function is a crucial ingredient for the theoretical study of modern photonic quantum devices, but is often difficult or even impossible to calculate directly. We present a numerically efficient framework for…
We discuss 1-dimensional Schrodinger operators with complex and locally integrable potentials that may have an arbitrary behavior at (finite or infinite) endpoints. The main tool of our analysis are Green's operators, that is, their various…
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs…
We study estimates of the Green's function in $\mathbb{R}^d$ with $d \ge 2$, for the linear second order elliptic equation in divergence form with variable uniformly elliptic coefficients. In the case $d \ge 3$, we obtain estimates on the…
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…
Dyadic Green's function is an important tool of computational photonics, giving deeper insights into light-matter interaction. We present an operator approach to the derivation of the dyadic Green's function of a generic anisotropic…
Closed expression for the Green's function of the stationary two-dimensional Schrodinger equation for an electron in group-VI dichalcogenides in the presence of a magnetic field is obtained in terms of the Whittaker functions. The resulting…
We derive formulas for the matrix elements of the two dimensional square lattice Green function along the diagonal, and along the coordinate axes. We also give an asymptotic formula for the diagonal elements.
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…
This work is a continuation and extension of the note published in the Russian Math Surveys 1997 n 6. For any pair of solutions of the spectral problem for the second order selfadjoint real Schrodinger Operator on the graph their Symplectic…
We describe two-dimensional potential Schrodinger and Dirac operators which are finite-gap at one energy level and have singular spectral curves. It appears that the singularities can be rather complicated. Such Dirac operators appear as…
The 2D space-fractional Schrodinger equation in the time-independent and time-dependent cases for the scattering problem in the fractional quantum mechanics is studied. We define and give the mathematical expression of the Green's functions…
We consider the Green's functions associated to a scalar field propagating on a curved, ultra-static background, in the presence of modified dispersion relations. The usual proper-time deWitt-Schwinger procedure to obtain a series…
This paper extends an earlier high-temperature lattice calculation of the renormalized Green's functions of a $D$-dimensional Euclidean scalar quantum field theory in the Ising limit. The previous calculation included all graphs through…
Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method of spectral analysis on self-similar graphs. We give an…
A numerical method is developed for calculating the real time Green's functions of very large sparse Hamiltonian matrices, which exploits the numerical solution of the inhomogeneous time-dependent Schroedinger equation. The method has a…