相关论文: Some observations on the Green function for the ba…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
In this paper, we derive certain formulas giving the Laplace transforms of two generalized fractional integral operators introduced recently in [Fract. Calc. Appl. Anal. 20 (2) (2017), 422--446]. The main results provide generalizations to…
The objective of the present paper is to give a survey of recent progress on applications of the approaches of Ringel-Hall type algebras to quantum groups and cluster algebras via various forms of Green's formula. In this paper, three forms…
The inversion of nabla Laplace transform, corresponding to a causal sequence, is considered. Two classical methods, i.e., residual calculation method and partial fraction method are developed to perform the inverse nabla Laplace transform.…
We propose a quadrature-based formula for computing the exponential function of matrices with a non-oscillatory integral on an infinite interval and an oscillatory integral on a finite interval. In the literature, existing quadrature-based…
We consider a two-dimensional diffusion process in a two-layered plane, governed by distinct covariance matrices in the upper and lower half-planes and by two drift vectors pointed away from the $x$-axis. We first analyze the case where the…
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…
In this paper, we prove an averaged version of an algebraicity conjecture in \cite{GKZ87} concerning the values of higher Green's function at CM points. Furthermore, we give the factorization of the ideal generated by such algebraic value…
We derive explicit representation formulae of Green functions for GJMS operators on $n$-spheres, including the fractional ones. These formulae have natural geometric interpretations concerning the extrinsic geometry of the round sphere.…
We derive a method to efficiently compute the Green function of on arbitrary Hamiltonians defined on semi-infinite and periodic quasi-one-dimensional lattices. Computing the Green function is the backbone of quantum transport, electronic…
Green's function methods lead to ab initio, systematically improvable simulations of molecules and materials while providing access to multiple experimentally observable properties such as the density of states and the spectral function.…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
We present an efficient implementation of a surface Green's-function method for atomistic modeling of surfaces within the framework of density functional theory using a pseudopotential localized basis set approach. In this method, the…
The Green's function plays a crucial role when studying the nature of quantum many-body systems, especially strongly-correlated systems. Although the development of quantum computers in the near future may enable us to compute energy…
Generalizing the concept of primary fields, we find a new representation of the Virasoro algebra, which we call it a pseudo-conformal representation. In special cases, this representation reduces to ordinary- or logarithmic-conformal field…
An efficient calculation method is proposed for the face centered cubic (FCC) lattice Green function. The method is based on binomial expansion theorems, which is provide us establish analytical formulae through simple basic integrals. The…
A simple model of noninteracting electrons with a separable one-body potential is used to discuss the possible pole structure of single particle Green's functions for fermions on unphysical sheets in the complex frequency plane as a…
We study the one-dimensional Schr\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and…
This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…
In this work we perform a Green's function analysis of giant-dipole systems. First we derive the Green's functions of different magnetically field-dressed systems, in particular of electronically highly excited atomic species in crossed…