Related papers: Resonances over a potential well in an island
We study the scattering of solitons in the nonlinear Schroedinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The…
We study the distribution of resonances for discrete Hamiltonians of the form $H_0+V$ near the thresholds of the spectrum of $H_0$. Here, the unperturbed operator $H_0$ is a multichannel Laplace type operator on $\ell^2(\mathbb Z; \mathbb…
Recent advances in machine learning establish the ability of certain neural-network architectures called neural operators to approximate maps between function spaces. Motivated by a prospect of employing them in fundamental physics, we…
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 present a unitary multichannel model for $\bar{K}N$ scattering in the resonance region that fulfills unitarity. It has the correct analytical properties for the amplitudes once they are extended to the complex-$s$ plane and the partial…
This paper is concerned with the inverse elastic scattering problem for a random potential in three dimensions. Interpreted as a distribution, the potential is assumed to be a microlocally isotropic Gaussian random field whose covariance…
Non-exotic scalar-meson resonances in S-wave meson-meson scattering are studied in the light of a unitarised Schroedinger model. The resulting poles in the scattering matrices, by analytical continuation into the complex-energy plane, are…
We study high energy resonances for the operators $-\Delta +\delta_{\partial\Omega}\otimes V$ and $-\Delta+\delta_{\partial\Omega}'\otimes V\partial_\nu$ where $\Omega$ is strictly convex with smooth boundary, $V:L^2(\partial\Omega)\to…
We consider the defocusing nonlinear Schr{\"o}dinger equation in several space dimensions, in the presence of an external potential depending on only one space vari-able. This potential is bounded from below, and may grow arbitrarily fast…
One-dimensional scattering by a target with two internal degrees of freedom is investigated. The damping of resonance peaks and the associated appearance of the fluctuating background in the quantum inelastic scattering amplitudes are…
We consider a magnetic Schr\"odinger operator $H^h$, depending on the semiclassical parameter $h>0$, on a two-dimensional Riemannian manifold. We assume that there is no electric field. We suppose that the minimal value $b_0$ of the…
Let P be the operator $-\Delta+V$ on R^d, where $V$ is a real potential with several inverse square singularities. The usual non-trapping type high-frequency inequality on the truncated resolvent of $P$ is shown, using semi-classical…
The poles of the quantum scattering matrix (S-matrix) in the complex momentum plane have been studied extensively. Bound states give rise to S-matrix poles, and other poles correspond to non-normalizable anti-bound, resonance and…
We develop scattering theory in a non-commutative space defined by a $su(2)$ coordinate algebra. By introducing a positive operator valued measure as a replacement for strong position measurements, we are able to derive explicit expressions…
The semi-classical regime of standing wave solutions of a Schr\"odinger equation in presence of non-constant electric and magnetic potentials is studied in the case of non-local nonlinearities of Hartree type. It is show that there exists a…
The aim of the lecture is to briefly describe the mathematical background of scattering theory for two- and three-particle quantum systems. We discuss basic objects of the theory: wave and scattering operators and the corresponding…
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
We revisit scattering of electromagnetic waves from metallic and semiconducting cylinders in the framework of complex angular momentum techniques. We prove that "resonant surface polariton modes" are generated by a unique surface wave, i.e.…
We show that for a one-dimensional Schr\"odinger operator with a potential whose first moment is integrable the scattering matrix is in the unital Wiener algebra of functions with integrable Fourier transforms. Then we use this to derive…
A design of the resonance spin finter is suggested in form of a quantum well with three quantum wires attached. Explicit formula is suggested for transmission coefficients accross the well in terms of the resonance eigenfunction of the…