Related papers: Long range scattering for the Wave-Schr"odinger sy…
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,…
In this article we present a method to compute the scattering states of holes in spherical bands in the strong spin-orbit coupling regime. More precisely, we calculate scattering phase shifts and amplitudes of holes induced by defects in a…
We study singular Gibbs measures for the three-dimensional Schr\"odinger-wave system, also known as the Yukawa system. Our primary result is the phase transition between weak and strong coupling cases, a phenomenon absent in one- and…
We revisit the Cauchy problem of nonlinear massive Dirac equation with Yukawa type potentials $\mathcal F^{-1}\left[(b^2 + |\xi|^2)^{-1}\right]$ in 2 dimensions. The authors of \cite{tes2d, geosha} obtained small data scattering and large…
The study of the scattering data for a star-shape network of LC-transmission lines is transformed into the scattering analysis of a Schr\"odinger operator on the same graph. The boundary conditions coming from the Kirchhoff rules ensure the…
In this paper, we study the decoherence of a wave described by the solution to a Schroedinger equation with a time-dependent random potential. The random potential is assumed to have slowly decaying correlations. The main tool to analyze…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
In this paper we study 3-d Hartree type fractional Schr\"odin-ger equations: \begin{equation} i\partial_{t}u-|\nabla|^{\alpha}u = \lambda\left(|x|^{-\gamma} *| u|^{2} \right)u,\;\;1 < \alpha < 2,\;\;0 < \gamma < 3,\;\; \lambda \in \mathbb R…
We consider a class of wave-Schroedinger systems with a Zakharov-Schulman type coupling. This class of systems is indexed by a parameter gamma which measures the strength of the null form in the nonlinearity of the wave equation. The case…
In this paper, we study the dynamics behavior of the NLS system with three waves interaction in the energy space $H^1(\mathbb{R}^5) \times H^1(\mathbb{R}^5)\times H^1(\mathbb{R}^5) $. Inspired by B. Dodson and J. Murphy in…
In this paper we consider the Schr\"odinger operator in ${\mathbb R}^3$ with a long-range magnetic potential associated to a magnetic field supported inside a torus ${\mathbb{T}}$. Using the scheme of smooth perturbations we construct…
We consider 3d Schrodinger operator with long-range potential that has short-range radial derivative. The long-time asymptotics of non-stationary problem is studied and existence of modified wave operators is proved. It turns out, the…
For the Schr\"odinger equation with a general interaction term, which may be linear or nonlinear, time dependent and including charge transfer potentials, we prove the global solutions are asymptotically given by the sum of a free wave and…
We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We…
The extraction of scattering parameters from Euclidean simulations of a Yukawa model in a finite volume with periodic boundary conditions is analyzed both in non relativistic quantum mechanics and in quantum field theory.
We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. We prove that, in dimensions larger than 3, small…
We prove sharp $L^\infty$ decay and modified scattering for the Schr\"odinger-Bopp-Podolsky equation in $2$ and $3$ spatial dimensions with small initial data chosen from a weighted Sobolev space.
In this paper we study the scattering of non-radial solutions in the energy space to coupled system of nonlinear Schr\"{o}dinger equations with quadratic-type growth interactions in dimension five without the mass-resonance condition. Our…
The Helmholtz equation in one dimension, which describes the propagation of electromagnetic waves in effectively one-dimensional systems, is equivalent to the time-independent Schr\"odinger equation. The fact that the potential term…