Related papers: Functional integral method for potential scatterin…
We show that using the properties of the photon Green's function one can successfully describe the propagation of arbitrary nonclassical optical radiation through structured materials. In contrast to the similar input-output approach, our…
We compute the scattering amplitude for Schr\"odinger operators at a critical energy level, corresponding to the maximum point of the potential. We follow the wrok of Robert and Tamura, '89, using Isozaki and Kitada's representation formula…
In this paper we present a new highly efficient calculation method for the far field amplitude pattern that arises from scattering problems governed by the d-dimensional Helmholtz equation and, by extension, Schr\"odinger's equation. The…
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,…
The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…
When a strong magnetostatic field is present, vacuum effectively appears as a linear, uniaxial, dielectric-magnetic medium for small-magnitude optical fields. The availability of the frequency-domain dyadic Green function when the…
In effective field theory physical quantities, in particular observables, are expressed as a power series in terms of a small expansion parameter. For non-perturbative systems, for instance nuclear physics, this requires the…
The quantum theory can be formulated in the language of positive functionals on Weyl or Clifford algebra ($L$-functionals). It is shown that this language gives simple understanding of diagrams of Keldysh formalism (that coincide in our…
A Green's function formalism to analyze the scattering properties in confined geometries is developed. This includes scattering from a central field inside the guide created e.g. by impurities. For atomic collisions our approach applies to…
In QFT the effective potential is an important tool to study symmetry breaking phenomena. It is known that, in some theories, the canonical approach and the path-integral approach yield different effective potentials. In this paper we…
I present numerical study of an elastic scattering by solving second order differential equations of Schroedinger Equation for some types of central potential (eg. square well, Yukawa, and Woods-Saxon) to find the wave function inside the…
This paper presents a windowed Green function (WGF) method for the numerical solution of problems of elastic scattering by "locally-rough surfaces" (i.e., local perturbations of a half space), under either Dirichlet or Neumann boundary…
Asymptotic behavior of the scattering amplitude for two scalar particles by scalar, vector and tensor exchanges at high energy and fixed momentum transfers is reconsidered in quantum field theory. In the framework of the quasi-potential…
This article is devoted to studying the inverse scattering for the fractional Schr\"{o}dinger equation, and in particular we solve the Born approximation problem. Based on the ($p$,$q$)-type resolvent estimate for the fractional Laplacian,…
I analyze the algebraic patterns underlying the structure of scattering amplitudes in quantum field theory. I focus on the decomposition of amplitudes in terms of independent functions and the systems of differential equations the latter…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
An optimized Rayleigh-Schr\"{o}dinger expansion scheme of solving the functional Schr\"odinger equation with an external source is proposed to calculate the effective potential beyond the Gaussian approximation. For a scalar field theory…
We present a new expression of the scattering amplitude, valid for spherical absorbing objects, which leads to an improved version of the eikonal method outside the diffraction region. Limitations of this method are discussed and numerical…
An integral equation-based numerical method for scattering from multi-dielectric cylinders is presented. Electromagnetic fields are represented via layer potentials in terms of surface densities with physical interpretations. The existence…
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…