相关论文: Lattice Green Functions: the seven-dimensional fac…

Localised defect modes generated by a finite line defect composed of several masses, embedded an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. Several representations…

Existence and uniqueness of advanced and retarded fundamental solutions (Green's functions) and of global solutions to the Cauchy problem is proved for a general class of first order linear differential operators on vector bundles over…

Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann…

We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the…

We are using the finite-gap approach for the construction of the Schr\"{o}dinger operator discretization on a quad graph. The latter is represented by a two-dimensional integer sublattice in a $d$-dimensional space. The Green's function of…

In this paper, we develop discrete versions of Darboux transformations and Crum's theorems for two second order difference equations. The difference equations are discretised versions (using Darboux transformations) of the spectral problems…

We construct Green's functions for elliptic operators of the form $\mathcal{L}u=-\text{div}(A\nabla u+bu)+c\nabla u+du$ in domains $\Omega\subseteq\mathbb R^n$, under the assumption $d\geq\text{div}b$, or $d\geq\text{div}c$. We show that,…

Let $\D$ be the finite difference Laplacian associated to the lattice $\bZ^{d}$. For dimension $d\ge 3$, $a\ge 0$ and $L$ a sufficiently large positive dyadic integer, we prove that the integral kernel of the resolvent $G^{a}:=(a-\D)^{-1}$…

In this paper I propose the use of a lattice derivative operator that is equivalent to the ideal SLAC derivative operator in all lattice calculations, but without the prohibitively expensive computational cost of the latter. A pedagogical…

Using an expansion method in the variables $ x_i$ that appear in the $(n-1)$-dimensional integrals representing the $n$-particle contribution to the Ising square lattice model susceptibility $\chi$, we generate a long series of coefficients…

Many recent papers deal with the enumeration of 2-dimensional walks with prescribed steps confined to the positive quadrant. The classification is now complete for walks with steps in $\{0, \pm 1\}^2$: the generating function is D-finite if…

Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes -- particularly around black holes -- we show how, for certain classes of geometries, one might obtain its retarded or advanced…

We propose two ways for determining the Green's matrix for problems admitting Hamiltonians that have infinite symmetric tridiagonal (i.e. Jacobi) matrix form on some basis representation. In addition to the recurrence relation comming from…

Lattice geometries and random walks on them are of great interest for their applications in different fields such as physics, chemistry, and computer science. In this work, we focus on multi-headed lattices and study properties of the Green…

A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the…

We present a series of Darboux integrable discrete equations on the square lattice. Equations of the series are numbered with natural numbers $M$. All the equations have a first integral of the first order in one of directions of the…

A method to calculate exact Green's functions on lattices in various dimensions is presented. Expressions in terms of generalized hypergeometric functions in one or more variables are obtained for various examples by relating the resolvent…

We have designed a new multi-scale approach for Strongly Correlated Systems by combining the Dynamical Cluster Approximation (DCA) and the recently introduced dual-fermion formalism. This approach employs an exact mapping from a real…

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…

We present our study of the renormalization of the chromomagnetic operator,O(CM), which appears in the effective Hamiltonian describing Delta S = 1 transitions in and beyond the Standard Model. We have computed, perturbatively to one-loop,…