Related papers: The spectral shift function for planar obstacle sc…
Let $S(k)$ be the scattering matrix for a Schr\"odinger operator (Laplacian plus potential) on $\RR^n$ with compactly supported smooth potential. It is well known that $S(k)$ is unitary and that the spectrum of $S(k)$ accumulates on the…
Scattering and bound states for a spinless particle in the background of a kink-like smooth step potential, added with a scalar uniform background, are considered with a general mixing of vector and scalar Lorentz structures. The problem is…
A description of the NN scattering is constructed starting from the $\pi, \eta, \eta'$ pseudoscalar-, the $\rho, \phi, \omega$ vector-, and the $\varepsilon(600), a_0, f_0(1400)$ scalar - meson-nucleon coupling constants, which we obtain…
Transmission probabilities of the scattering problem with a position dependent mass are studied. After sketching the basis of the theory, within the context of the Schr\"{o}dinger equation for spatially varying effective mass, the simplest…
In a recent work, S.A.R. Horsley and coworkers [Nature Photon 9, 436-439 (2015)] showed rather interestingly that planar dielectric media, for which the real and imaginary parts of the dielectric permittivity are related by spatial…
We study the asymptotic behavior as L \to \infty of the finite-volume spectral shift function for a positive, compactly-supported perturbation of a Schr\"odinger operator in d-dimensional Euclidean space, restricted to a cube of side length…
The object of study in this paper is the on-shell scattering matrix $S(E)$ of the Schr\"odinger operator with the potential satisfying assumptions typical in the theory of shape resonances. We study the spectrum of $S(E)$ in the…
We study anisotropic fractional discrete Laplacians $\Delta_{\mathbb{Z}^d}^{\vec{\mathbf{r}}}$ with exponents $\vec{\mathbf{r}}\in\mathbb{R}^d\setminus\{0\}$ on $\ell^2(\mathbb{Z}^d)$. We establish a Mourre estimate on compact energy…
The analysis of semi-inclusive deep inelastic electron scattering off polarized $^3$He at finite momentum transfers, aimed at the extraction of the quark transverse-momentum distributions in the neutron, requires the use of a distorted…
We give a simple definition of a spectral shift function for pairs of nonpositive operators on Banach spaces and prove trace formulas of Lifshitz-Kre\u{\i}n type for a perturbation of an operator monotonic (negative complete Bernstein)…
We study the crossover from the one-dimensional to the two-dimensional Hubbard model in the photoemission spectra of weakly coupled chains. The chains with on-site repulsion are treated using the spin-charge factorized wave function, that…
We investigated the elastic scattering problem with deformed Heisenberg algebra leading to the existence of a minimal length. The continuity equations for the moving particle in deformed space were constructed. We obtained the Green's…
In this work, we study the propagation of scalar fields in the gravitational background of a higher-dimensional Schwarzschild-de-Sitter black hole as well as on the projected-on-the-brane 4-dimensional background. The scalar fields have…
The problem of diffraction by a Dirichlet quarter-plane (a flat cone) in a 3D space is studied. The Wiener-Hopf equation for this case is derived and involves two unknown (spectral) functions depending on two complex variables. The aim of…
Nonperturbative polaron variational methods are applied, within the so-called particle or worldline representation of relativistic field theory, to study scattering in the context of the scalar Wick - Cutkosky model. Important features of…
We study the spectra generated as a result of bulk Comptonization by relativistic electrons in radial flows onto compact objects. We solve numerically the general-relativistic radiative transfer equation in the Schwarzschild spacetime, in…
It is shown that the potential perturbation that shifts a chosen standing wave in space is a block of potential barrier and well for every wave bump between neighbouring knots. The algorithms shifting the range of the primary localization…
The hyperbolic version of Roy-Steiner equation describing low energy $\pi N$ scatterings, with larger analyticity domain in the complex $s$ plane is solved. The numerical results on phase shifts of low partial waves are in agreement with…
We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig-Merle for the $H^1$ critical wave and Schr\"odinger equations. Our result includes the $H^1$…
We investigate the phase shifts of low-energy alpha-alpha scattering under variations of the fundamental parameters of the Standard Model, namely the light quark mass, the electromagnetic fine-structure constant as well as the QCD…