Related papers: The spectral shift function for planar obstacle sc…
We show that submicron Silicon spheres, whose polarizabilities are completely given by their two first Mie coefficients, are an excellent laboratory to test effects of both angle-suppressed and resonant differential scattering cross…
For the 3D focusing cubic nonlinear Schrodinger equation, Scattering of $H^1$ solutions inside the (scale invariant) potential well was established by Holmer and Roudenko~\cite{HR2} (radial case) and Duyckaerts, Holmer and…
The speed-dependent spectral line profiles collapse into a simple Lorentz profile in the regime dominated by the velocity-changing collisions. We derive general formulas for the effective width and shift of the Lorentzian for arbitrary…
In this paper we study the asymptotic expansion of the spectral shift function for the slowly varying perturbations of periodic Schr\"odinger operators. We give a weak and pointwise asymptotics expansions in powers of $h$ of the derivative…
We investigate the scattering of a spinning test particle by a Kerr black hole within the Mathisson-Papapetrou-Dixon model to linear order in spin. The particle's spin and orbital angular momentum are taken to be aligned with the black…
We present a novel analysis of the $\pi N$ scattering amplitude in covariant baryon chiral perturbation theory up to ${\cal O}(p^3)$ within the extended-on-mass-shell renormalization scheme and including the $\Delta(1232)$ explicitly in the…
The Friedrichs model~\cite{Friedrichs} is revisited to obtain precise results about the asymptotic behaviour (the so-called Breit-Wigner formula~\cite{Breit}) of a resonance near an embedded eigenvalue and the ``spectral concentration"…
Scattering phase shift, as a key parameter in scattering theory, plays an important role in characterizing low-energy collisions between ultracold atoms. In this work, we theoretically investigate the universal low-energy behavior of the…
We argue that, as a consequence of the graviton's spin-2, its bremsstrahlung in trans-planckian-energy ($E\gg M_P$) gravitational scattering at small deflection angle can be nicely expressed in terms of helicity-transformation phases and…
We show that the conformally invariant fractional powers of the sub-Laplacian on the Heisenberg group are given in terms of the scattering operator for an extension problem to the Siegel upper halfspace. Remarkably, this extension problem…
We improve, in the energy region between $\bar{K}K$ threshold and $\sim~1.4$ GeV, the energy-dependent phase shift analysis of $\pi\pi$ scattering presented in a previous paper. For the S0 wave we have included more data above $\bar{K}K$…
We determine the low-energy behaviour of the scattering operator of two-dimensional Schr\"odinger operators with any type of obstructions at 0-energy. We also derive explicit formulas for the wave operators in the absence of p-resonances,…
For scattering off a smooth, strictly convex obstacle $\Omega \subset \mathbb{R}^d$ with positive curvature, we show that the eigenvalues of the scattering matrix -- the phase shifts -- equidistribute on the unit circle as the frequency $k…
The ultrarelativistic limit of the Kerr - Newman geometry is studied in detail. We find the gravitational shock wave background associated with this limit. We study the scattering of scalar fields in the gravitational shock wave geometries…
We consider a second order difference equation with operator-valued coefficients. More precisely, we study either compact or trace class perturbations of the discrete Laplacian in the Hilbert space of bi-infinite square-summable sequence…
The Wigner time delay of slow particles in the process of their elastic scattering by complex targets formed by several zero-range potentials is investigated. It is shown that at asymptotically large distances from the target, the…
The spectrum of the spherically symmetric alpha-2 dynamo is studied in the case of idealized boundary conditions. Starting from the exact analytical solutions of models with constant alpha-profiles a perturbation theory and a Galerkin…
In this survey article we consider the operator pair $(H,H_0)$ where $H_0$ is the shifted 3D Schr\"odinger operator with constant magnetic field, $H : = H_0 + V$, and $V$ is a short-range electric potential of a fixed sign. We describe the…
The Kohn variational principle and the hyperspherical harmonic technique are applied to study p-3He elastic scattering at low energies. Preliminary results obtained using several interaction models are reported. The calculations are…
Tunable directional scattering is of paramount importance for operation of antennas, routing of light, and design of topologically protected optical states. For visible light scattered on a nanoparticle the directionality could be provided…