Related papers: Multi-headed lattices and Green functions
In a recent series of scanning probe experiments, it became possible to visualize local electron flow in a two-dimensional electron gas. In this paper, a Green's function technique is presented that enables efficient calculation of the…
We consider a variety of settings involving chains with one or more defects stemming from the introduction of nodes bearing internal resonators. Motivated by experimental results in woodpile elastic lattices with one or two defects, we…
Lattices abound in nature - from the crystal structure of minerals to the honey-comb organization of ommatidia in the compound eye of insects. Such regular arrangements provide solutions for optimally dense packings, efficient resource…
We discuss a class of problems which we call lattice exit models. At one level, these problems provide undergraduate level exercises in labeling the vertices of graphs (e.g., depth first search). At another level (theorems about large scale…
In order to investigate the dependence on lattice size of several observables in percolation, the Hoshen-Kopelman algorithm was modified so that growing lattices could be simulated. By this way, when simulating a lattice of size L, lattices…
Green's functions are highly useful in analyzing the dynamical behavior of polynomials in their escaping set. The aim of this paper is to construct an analogue of Green's functions for planar quasiregular mappings of degree two and constant…
Green's functions characterize the fundamental solutions of partial differential equations; they are essential for tasks ranging from shape analysis to physical simulation, yet they remain computationally prohibitive to evaluate on…
The hierarchy of Green functions for (quasi)degenerate systems, presented in cond-mat/0308058, is calculated in detail for the case of a system with closed shells plus a single electron in a two-fold degenerate level. The complete hierarchy…
This survey addresses pluri-periodic harmonic functions on lattices with values in a positive characteristic field. We mention, as a motivation, the game "Lights Out" following the work of Sutner, Goldwasser-Klostermeyer-Ware,…
In this work we analyze the statistical thermodynamics of Diced lattice carriers employing a Greens function formulation to examine the grand potential, Helmholtz free energy, the grand and ordinary partition functions and entropy. This…
We investigate the limits of the ideals of holomorphic functions vanishing on three points in $\C^2$ when all three points tend to the origin, and what happens to the associated pluricomplex Green functions. This is a continuation of the…
We develop a Green's function approach to compute R\'{e}nyi entanglement entropy on lattices and fuzzy spaces. The R\'{e}nyi entropy resulting from tracing out an arbitrary collection of subsets of coupled harmonic oscillators is written as…
Sub-wavelength arrays of quantum emitters offer an efficient free-space approach to coherent light-matter interfacing, using ultracold atoms or two-dimensional solid-state quantum materials. The combination of collectively suppressed…
Basing on the relation between the Coulomb Green function and the Green function of harmonic oscillator, the algebraic representation of the many-particle Coulomb Green function in the form of annihilation and creation operators is…
Several classic problems for particles diffusing outside an arbitrary configuration of non-overlapping partially reactive spherical traps in three dimensions are revisited. For this purpose, we describe the generalized method of separation…
Recent breakthroughs in the experimental manipulation of strongly interacting atomic Rydberg gases in lattice potentials have opened a new avenue for the study of many-body phenomena. Considerable efforts are currently being undertaken to…
Stieltjes boundary problems generalize the customary class of well-posed two-point boundary value problems in three independent directions, regarding the specification of the boundary conditions: (1) They allow more than two evaluation…
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.
Several widely used methods for the calculation of band structures and photo emission spectra, such as the GW approximation, rely on Many-Body Perturbation Theory. They can be obtained by iterating a set of functional differential equations…
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…