Related papers: Green's Functions For Random Resistor Networks
In calculating Green functions for interacting quantum systems numerically one often has to resort to finite systems which introduces a finite size level spacing. In order to describe the limit of system size going to infinity correctly,…
For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…
We develop a nonperturbative dynamical theory (NDT) to calculate the retarded Green's function under nonequilibrium conditions. The NDT is particularly useful for treating nonequilibrium transport problems in systems with strong…
Lattice Green's Functions (LGFs) are fundamental solutions to discretized linear operators, and as such they are a useful tool for solving discretized elliptic PDEs on domains that are unbounded in one or more directions. The majority of…
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks…
The effect of disorder on the perpendicular magnetoresistance of magnetic multilayers is investigated theoretically. Various kinds of disorder are considered: (i) interface substitutional disorder and (ii) bulk disorder in the various…
We calculate the effective resistance between two arbitrary lattice points on infinite strip of the triangular lattice (ladder network) in one dimension, and on infinite modified square and Union Jack lattices in two dimensions, and on…
We consider the problem of wave propagation for a 2-D rectilinear optical waveguide which presents some perturbation. We construct a mathematical framework to study such a problem and prove the existence of a solution for the case of small…
Disorder is a key factor influencing the behavior of condensed states of matter, however the true extent of its impact is generally difficult to determine due to the prominent roles played by quantum interference, entanglement between spin…
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…
It is common in the accelerator community to use the impedance of accelerator components to describe wake interactions in the frequency domain. However, it is often desirable to understand such wake interactions in the time domain in a…
We study statistics of resonances in a one-dimensional disordered chain coupled to an outer world simulated by a perfect lead. We consider a limiting case for weak disorder and derive some results which are new in these studies. The main…
The algorithm to calculate the generating function for the number of ``skeleton'' diagrams for the irreducible self-energy and vertex parts is derived for the problems with Gaussian random fields. We find an exact recurrence relation…
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…
Disordered networks of fragile elastic elements have been proposed as a model of inner porous regions of large bones [Gunaratne et.al., cond-mat/0009221, http://xyz.lanl.gov]. It is shown that the ratio $\Gamma$ of responses of such a…
Resonance is a well-known phenomenon that happens in systems with second order dynamics. In this paper we address the fundamental question of making a network robust to signal being periodically pumped into it at or near a resonant…
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…
We discuss random matrix models in terms of elementary operations on Blue's functions (functional inverse of Green's functions). We show that such operations embody the essence of a number of physical phenomena whether at/or away from the…
An analytical Green's function is developed to study the acoustic scattering by a flat plate with a serrated edge. The scattered pressure is solved using the Wiener-Hopf technique in conjunction with the adjoint technique. It is shown that…