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Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual…
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 magnetic inverse source problem of reconstructing the positions and currents of very long parallel conductors is considered in a two-dimensional situation, with applications to power line measurements. The input data is the magnetic…
We develop an algorithm that forecasts cascading events, by employing a Green's function scheme on the basis of the self-exciting point process model. This method is applied to open data of 10 types of crimes happened in Chicago. It shows a…
We prove a connection between the Green's function of the fractional Anderson model and the two point function of a self-avoiding random walk with long range jumps, adapting a strategy proposed by Schenker in 2015. This connection allows us…
A stochastic method is described for estimating Green's functions (GF's), appropriate to linear advection-diffusion-reaction transport problems, evolving in arbitrary geometries. By allowing straightforward construction of approximate,…
We demonstrate an efficient nonequilibrium Green's function transport calculation procedure based on the real-space finite-difference method. The direct inversion of matrices for obtaining the self-energy terms of electrodes is…
With a super-high-efficient numerical algorithm, we are able to self-consistently calculate the Green's function in the renormalized-ring-diagram approximation for a two-dimensional electron system with long-range Coulomb interactions. The…
Spectral methods have myriad applications in high-dimensional statistics and data science, and while previous works have primarily focused on $\ell_2$ or $\ell_{2,\infty}$ eigenvector and singular vector perturbation theory, in many…
The equation of motion method (EOM) for Green functions is one of the tools used in the analysis of quantum dot system coupled with metallic and superconducting leads. We investigate modified EOM, based on differentiation of double-time…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…
The real part of the self-energy of interacting two-dimensional electrons has been calculated in the t-matrix approximation. It is shown that the forward scattering results in an anomalous term leading to the vanishing renormalization…
We show how two-point correlation functions derived within non-isotropic random wave models are in fact quantum results that are obtained in the appropriate limit in terms of the exact Green function of the quantum system. Since no…
Derivative Free Optimization is known to be an efficient and robust method to tackle the black-box optimization problem. When it comes to noisy functions, classical comparison-based algorithms are slower than gradient-based algorithms. For…
We present a comprehensive study for common second order PDE's in two dimensional disk-like systems and show how their solution can be approximated by finding the Green function of an effective one dimensional system. After elaborating on…
Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…
This short paper is concerned with the numerical reconstruction of small sources from boundary Cauchy data for a single frequency. We study a sampling method to determine the location of small sources in a very fast and robust way.…
Within the framework of many-particle perturbation theory, we develop an analytical approach that allows us to determine the small distance behavior of Green's functions and related quantities in electronic structure theory. As a case…
We create virtual sources and receivers in a 3D subsurface using the previously derived single-sided homogeneous Green's function representation. We employ Green's functions and focusing functions that are obtained using reflection data at…
The two-time Green function method in quantum electrodynamics of high-Z few-electron atoms is described in detail. This method provides a simple procedure for deriving formulas for the energy shift of a single level and for the energies and…