Related papers: Wave propagation on a random lattice
This paper examines the propagation of time-harmonic waves in a two-dimensional triangular lattice with a lattice constant $a = 1$. The sources are positioned along line segments within the lattice. Specifically, we investigate the discrete…
We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation,…
The multiple scattering model of a quantum particle in a random Lorentz gas consisting of fixed point scatterers is considered in arbitrary dimension. An efficient method is developed to numerically compute the map of the density of…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
We present quantum Lattice Boltzmann simulations of the Dirac equation for quantum-relativistic particles with random mass. By choosing zero-average random mass fluctuation, the simulations show evidence of localization and ultra-slow Sinai…
In this work we develop a Monte Carlo method to compute the height distribution of local maxima of a stationary Gaussian or Gaussian-related random field that is observed on a regular lattice. We show that our method can be used to provide…
We derive a generalized linear dispersion relation of waves in a strongly magnetized, compressible, homogeneous and isotropic quasineutral plasma. Starting from a two fluid model, describing distinguishable electron and ion fluids, we…
The theory of scattering of atom pairs in a periodic potential is presented for the case of different atoms. When the scattering dynamics is restricted to the lowest Bloch band of the periodic potential, a separation in relative and average…
We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which…
We implement a proposal made in [arXiv:1107.4388] to determine the lattice spacing by matching the lattice vector correlator at a reference distance scale with the same correlator obtained by a dispersion relation based on the $R$-ratio…
Here to represent the propagation of waves I attempted to describe them separately in space and time domains. The time and space wave equations are obtained and investigated, and formulas for the wave propagation are expressed. I also tried…
Analytic expressions for the fields of a radially polarized, ultrashort and tightly focused laser pulse propagating in a linear-response plasma are derived and discussed. The fields are obtained from solving the inhomogenous wave equations…
We study the transport of a quantum particle through square lattices of various sizes by employing the tight-binding Hamiltonian from quantum percolation. Input and output semi-infinite chains are attached to the lattice either by diagonal…
The quasi-one-dimensional rhombic array of the waveguides is considered. System of equations describing coupled waves in the waveguide in the linear limit is solved exactly. The electric field distribution was found both for the…
We give a general procedure for extracting the propagators in gauge theories in presence of a sharp gauge fixing and we apply it to derive the propagators in quantum gravity in the radial gauge, both in the first and in the second order…
This paper has few different, but interrelated, goals. At first, we will propose a version of discretization of quantum field theory (Chapter 3). We will write down Lagrangians for sample bosonic fields (Section 3.1) and also attempt to…
A number of equations is deduced which describe propagation of excitations along $n$-dimensional surfaces in $R^N$. Usual excitations in wave theory propagate along 1-dimensional trajectories. The role of the medium of propagation of…
By using a small rotation approach, we show that it is possible to obtain well behaved perturbed solutions for the amplitude of the electromagnetic field propagating in a photonic waveguide array. This array mimics the propagation of a…
We analyze one-dimensional photonic superlattices which alternate layers of air and a left-handed material. We assume Drude-type dispersive responses for the dielectric permittivity and magnetic permeability of the left-handed material.…
The propagation of high-frequency gravitational waves can be analyzed using the geometrical optics approximation. In the case of large but finite frequencies, the geometrical optics approximation is no longer accurate, and…