相关论文: Lattice Green Functions: the seven-dimensional fac…
We present a method for calculating the complex Green function $G_{ij} (\omega)$ at any real frequency $\omega$ between any two sites $i$ and $j$ on a lattice. Starting from numbers of walks on square, cubic, honeycomb, triangular, bcc,…
We have studied possible applications of a particular pseudo-differential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The…
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.
We build upon a recent theoretical breakthrough by employing novel algorithms to accurately compute the fractions $F_p$ of all closed walks on the infinite square lattice whose the last erased loop corresponds is any one of the $762, 207,…
An expression for the Green's function (GF) of anisotropic face centered cubic lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are…
The availability of efficient Krylov subspace solvers play a vital role for the solution of a variety of numerical problems in computational science. Here we consider lattice field theory. We present a new general numerical method to…
The lattice Green function, i.e., the resolvent of the discrete Laplace operator, is fundamental in probability theory and mathematical physics. We derive its long-distance behaviour via a detailed analysis of an integral representation…
The generating function for recurrent Polya walks on the four dimensional hypercubic lattice is expressed as a Kampe-de-Feriet function. Various properties of the associated walks are enumerated.
Lattice Green's functions (LGF) and density of states (DOS) for non-interacting models on 3 related lattices are presented. The DOS and LGF at the origin for the kagome and diced lattices are rederived. Furthermore, from the form obtained…
In this paper we shall propose a simple scheme for calculating Green's functions for photons propagating in complex structured dielectrics or other photonic systems. The method is based on an extension of the finite difference time domain…
Flexible boundary condition methods couple an isolated defect to bulk through the bulk lattice Green's function. The inversion of the force-constant matrix for the lattice Green's function requires Fourier techniques to project out the…
Computing the atomic geometry of lattice defects--point defects, dislocations, crack tips, surfaces, or boundaries--requires an accurate coupling of the local strain field to the long-range elastic field. Periodic boundary conditions used…
We consider a divergence-form elliptic difference operator on the lattice $\mathbb{Z}^d$, with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently, Bourgain introduced novel techniques from harmonic analysis…
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…
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…
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…
A new expression for the Green's function of a finite one-dimensional lattice with nearest neighbor interaction is derived via discrete Fourier transform. Solution of the Heisenberg spin chain with periodic and open boundary conditions is…
A lattice QCD calculation for the four gluon one-particle irreducible Green function in the Landau gauge is discussed. Results for some of the associated form factors are reported for kinematical configurations with a single momentum scale.…
We construct Green's function for second order elliptic operators of the form $Lu=-\nabla \cdot (\mathbf{A} \nabla u + \boldsymbol{b} u)+ \boldsymbol c \cdot \nabla u+ du$ in a domain and obtain pointwise bounds, as well as Lorentz space…
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…