相关论文: Multi-headed lattices and Green functions
The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two…
We generalize the methods used in the theory of correlation dynamics and establish a set of equations of motion for many-body correlation green's functions in the non-relativistic case. These non-linear and coupled equations of motion…
We previously reported on a recursive method to generate the expansion of the lattice Green function of the $d$-dimensional face-centred cubic lattice (fcc). The method was used to generate many coefficients for d=7 and the corresponding…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…
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…
We present a further development of methods for analytical calculations of Green's functions of lattice fermions based on recurrence relations. Applying it to tight-binding systems and topological superconductors in different dimensions we…
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…
We study several quantities associated to the Green's function of a multiply connected domain in the complex plane. Among them are some intrinsic properties such as geodesics, curvature, and $L^2$-cohomology of the capacity metric and…
We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs…
The Green-function technique, termed the irreducible Green functions (IGF) method, that is a certain reformulation of the equation-of motion method for double-time temperature dependent Green functions is presented. This method was…
This paper studies the asymptotic behavior of the Green function of a multidimensional random walk killed when leaving a convex cone with smooth boundary. Our results imply uniqueness, up to a multiplicative factor, of the positive harmonic…
We show that the Green functions on flat tori can have either 3 or 5 critical points only. There does not seemto be any directmethod to attack this problem. Instead, we have to employ sophisticated non-linear partial differential equations…
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 derive general relations for the band-structure of an array of quantum dots and compute its transport properties when connected to two perfect leads. The exact lattice Green's functions for the perfect array and with an…
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.
Coincidence Site Lattices (CSLs) are a well established tool in the theory of grain boundaries. For several lattices up to dimension $d=4$, the CSLs are known explicitly as well as their indices and multiplicity functions. Many of them…
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…
We show how to use the lattice Green function to calculate capacitances in two dimensions with boundary conditions at infinity. It is shown how to calculate coefficients of capacitance and induction from the lattice Green function. A…
Trying to enumerate all of the walks in a 2D lattice is a fun combinatorial problem and there are numerous applications, from polymers to sports. Computers provide a wonderful tool for analyzing these walks; we provide a Maple package for…
In a recent letter [Phys. Rev. Lett. 131, 216401] we presented the multichannel Dyson equation (MCDE) in which two or more many-body Green's functions are coupled. In this work we will give further details of the MCDE approach. In…