Related papers: A note on double Floquet-Bloch transforms and the …
We study the poles of the retarded Green's functions of strongly coupled field theories exhibiting a variety of phase structures from a crossover up to a first order phase transition. These theories are modeled by a dual gravitational…
For Hamitonian systems with 3/2 degrees of freedom close to nonlinear integrable and for symplectic maps of the cylinder, bifurcations in degenerate resonance zones are discussed.
Precise asymptotics known for the Green's function of the Laplace operator have found their analogs for periodic elliptic operators of the second order at and below the bottom of the spectrum. Due to the band-gap structure of the spectra of…
In this work we analyze the complex scaling method applied to the problem of time-harmonic scalar wave propagation in junctions between `leaky,' or open dielectric waveguides. In [arXiv:2302.04353, arXiv:2310.05816, arXiv:2401.04674,…
The goal of this paper is to provide an intuitive and useful tool for analyzing the impurity bound state problem. We develop a semiclassical approach and apply it to an impurity in two dimensional systems with parabolic or Dirac like bands.…
In this note, we are concerned with the asymptotic approximation of a class of double integrals which can be represented as an angular spectrum superposition. These double integrals typically appear in electromagnetic scattering problems.…
The fundamental solution (Green function) for the Cauchy problem of the space-time fractional diffusion equation is investigated with respect to its scaling and similarity properties, starting from its Fourier-Laplace representation. Then,…
Inclusive and diffractive structure functions for electron-proton scattering are calculated in a semiclassical approach at large momentum transfer $Q^2$ and small values of the scaling variable $x$. The basic process is the production of a…
We consider the Faddeev-Green function in the three-dimensional space and in a slab, and we construct formal asymptotic expansions for the large complex parameter appearing in this function. The basic idea of the construction is to express…
A key issue in the solution of partial differential equations via integral equation methods is the evaluation of possibly singular integrals involving the Green's function and its derivatives multiplied by simple functions over discretized…
The numerical approximation of some Boussinesq systems in two spatial dimensions is here considered. The differential systems under study are proposed as asymptotic models for the propagation of waves along the interface of two layers of…
We report a new computational method based on the recursive Green's function technique for calculation of light propagation in photonic crystal structures. The advantage of this method in comparison to the conventional finite-difference…
Green's function provides an inherent connection between theoretical analysis and numerical methods for elliptic partial differential equations, and general absence of its closed-form expression necessitates surrogate modeling to guide the…
This paper introduces a fast algorithm, applicable throughout the electromagnetic spectrum, for the numerical solution of problems of scattering by periodic surfaces in two-dimensional space. The proposed algorithm remains highly accurate…
We establish the relation between full traces of the Green functions for some initial and the Darboux transformed one-dimensional two component Dirac problems with the most general form of potential. The result is used to check the…
We are looking at a Dirac electron in the electromagnetic field of a plane monochrome polarized X-ray. It will be attempted to link the terms of a certain (joint) asymptotic expansion of the Heisenberg propagations of momentum- and…
In this paper we study the asymptotic behaviour via Gamma-convergence of some integral functionals which model some multi-dimensional structures and depend explicitly on the linearized strain tensor. The functionals are defined in…
We consider the transmission of massless Dirac fermions through an array of short range scatterers which are modeled as randomly positioned $\delta$- function like potentials along the x-axis. We particularly discuss the interplay between…
We consider the two-dimensional high-frequency plane wave scattering problem in the exterior of a finite collection of disjoint, compact, smooth, strictly convex obstacles with Neumann boundary conditions. Using integral equation…
With a non-unitary transformation, the Lagrangian of a Dirac fermion is decomposed into two decoupled sectors. We propose to describe massive relativistic fermions in gauge theories in a two-component form. All relations between the Green's…