相关论文: Some observations on the Green function for the ba…

The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…

In this paper, we resort to the Laplace transform method in order to show its efficiency when approaching some types of fractional differential equations. In particular, we present some applications of such methods when applied to possible…

We give a very simple proof of the positivity and unimodality of the Green function for the killed fractional Laplacian on the periodic domain. The argument relies on the Jacobi triple product and a probabilistic representation of the Green…

This paper is devoted to the Laplacian operator of fractional order $s\in (0,1)$ in several dimensions. We first establish a representation formula for the partial derivatives of the solutions of the homogeneous Dirichlet problem. Along the…

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…

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…

The basic mathematical properties of Green's functions used in statistical mechanics as well as the equations defining these functions and the techniques of solving these equations are reviewed. An approach is presented called the…

Using a recently developed approach for solving the three dimensional Dirac equation with spherical symmetry, we obtain simple representations for the Green's function of the Dirac-Oscillator and Dirac-Coulomb problems. This is accomplished…

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.…

A new approach proposed recently by author for the calculation of Green functions in quantum field theory and quantum mechanics is briefly reviewed. The method is applied to nonperturbative calculations for anharmonic oscillator,…

In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…

We use a lattice Green function approach to study the stationary modes of a linear/nonlinear (Kerr) impurity embedded in a periodic one-dimensional lattice where we replace the standard discrete Laplacian by a fractional one. The energies…

We introduce a general scheme to consistently truncate equations of motion for Green's functions. Our scheme is guaranteed to generate physical Green's functions with real excitation energies and positive spectral weights. There are free…

In this article, we consider a nabla fractional boundary value problem with general boundary conditions. Brackins \& Peterson \cite{Br} gave an explicit expression for the corresponding Green's function. Here, we show that this Green's…

In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theory are given. In particular we evaluate…

In this paper, we summarize the technique of using Green functions to solve electrostatic problems. We start by deriving the electric potential in terms of a Green function and a charge distribution. We then provide a variety of example…

We develop a new algebraic setting for treating piecewise functions and distributions together with suitable differential and Rota-Baxter structures. Our treatment aims to provide the algebraic underpinning for symbolic computation systems…

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…

The Green's function formalism in Condensed Matter Physics is reviewed within the equation of motion approach. Composite operators and their Green's functions naturally appear as building blocks of generalized perturbative approaches and…

We consider a massive relativistic particle in the background of a gravitational plane wave. The corresponding Green functions for both spinless and spin 1/2 cases, previously computed by A. Barducci and R. Giachetti \cite{Barducci3}, are…