Related papers: Averaging in scattering problems
Infinitely rising one-dimensional potentials constitute impenetrable barriers which reflect totally any incident wave. However, the scattering by such kind of potentials is not structureless: resonances may occur for certain values of the…
We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this…
Medium and high energy absorptive parts contribute to dispersive expressions for D- wave scattering lengths, $a^0_2$ and $a^2_2$. For the model employed by Basdevant, Frogatt and Peterson we find the D- wave driving term contributions to…
In this paper, we continue our study [16] on the long time dynamics of radial solutions to defocusing energy critical wave equation with a trapping radial potential in 3 + 1 dimensions. For generic radial potentials (in the topological…
Electromagnetic scattering on a sphere is one of the most fundamental problems, which has a closed form analytical solution in the form of Mie series. Being initially formulated for a plane incident wave, the formalism can be extended to…
We show that high energy scattering is a statistical process essentially similar to reaction-diffusion in a system made of a finite number of particles. The Balitsky-JIMWLK equations correspond to the time evolution law for the particle…
We discuss the general behavior of the near-threshold scattering amplitude with channel couplings. The signal of the exotic hadrons near the threshold may manifest as a dip structure in the cross section originated from a zero point of the…
Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in general spatial dimension $D\geq 1$ when the density of states…
Motivated by applications to acoustic imaging, the present work establishes a framework to analyze scattering for the one-dimensional wave, Helmholtz, Schr\"odinger and Riccati equations that allows for coefficients which are more singular…
The radiation condition is the key question in the mathematical modelling for scattering problems in unbounded domains. Mathematically, it plays the role as the "boundary condition" at the infinity, which guarantees the well-posedness of…
We show that the Bethe-Salpeter equation for the scattering amplitude in the limit of zero incident energy can be transformed into a purely Euclidean form, as it is the case for the bound states. The decoupling between Euclidean and…
Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of…
We consider the focusing generalized Hartree equation in $H^1(\R^3)$ with a potential, \begin{equation*} iu_t + \Delta u - V(x)u + (I_\gamma \ast |u|^p )|u|^{p-2} u=0, \end{equation*} where $I_\gamma = \frac{1}{|x|^{3-\gamma}}$, $p \geq 2$…
In the three-body problem with positive energy, solutions which avoid triple collision have the property that the size of the triangle formed by the bodies tends to infinity as $t\rightarrow \pm\infty$. Furthermore, the triangles have…
The extended boundary condition method can be formulated to study plane-wave scattering by an ellipsoid composed of an orthorhombic dielectric-magnetic material whose relative permittivity dyadic is a scalar multiple of its relative…
The algebraic approach to the phase problem for the case of X-ray scattering from an ideal crystal is extended to the case of the neutron scattering, overcoming the difficulty related to the non-positivity of the scattering density. In this…
We propose parameterization procedures of the scattering amplitude f_{1+}^{3}(s)) with a view to extracting the pole parameters from data in the elastic region of {\pi}N scattering. This is achieved by considering the analyticity properties…
The scattering of quasiperiodic waves for a two-dimensional Helmholtz equation with a constant refractive index perturbed by a function which is periodic in one direction and of finite support in the other is considered. The scattering…
Scattering processes are a fundamental way of experimentally probing distributions and properties of systems in several areas of physics. Considering two-body scattering at low energies, when the de Broglie wavelength is larger than the…
A rigorous theory of diffraction scattering from extended objects is proposed. The present theory is based on a multiple asymptotic expansion of an integral equation for the exact wave function in terms of the large parameters of the…