Related papers: Semiclassical analysis of low and zero energy scat…
We consider a quantum system S interacting with another system S and susceptible of being absorbed by S. The effective, dissipative dynamics of S is supposed to be generated by an abstract pseudo-Hamiltonian of the form H = H0 + V -- iC *…
We study the infimum of the spectrum, or ground state energy (g.s.e.), of a discrete Schr\"odinger operator on $\theta\mathbb{Z}^d$ parameterized by a potential $V:\mathbb{R}^d\rightarrow\mathbb{R}_{\ge 0}$ and a frequency parameter…
The inverse scattering approach for the defocusing Davey-Stewartson II equation is given by a system of D-bar equations. We present a numerical approach to semi-classical D-bar problems for real analytic rapidly decreasing potentials. We…
This paper presents and discusses the conditions for zero electromagnetic scattering by electrically small particles. We consider the most general bi-anisotropic particles, characterized by four dyadic polarizabilities and study the case of…
We consider the scattering of time-harmonic electromagnetic waves by a penetrable thin tubular scattering object in three-dimensional free space. We establish an asymptotic representation formula for the scattered wave away from the thin…
We consider the asymptotics of the one-dimensional cubic nonlinear Schr\"odinger equation with an external potential $V$ that does not admit bound states. Assuming that $\jBra{x}^{2+}V(x) \in L^1$ and that $u$ is orthogonal to any…
Using a unitary extension of chiral perturbation theory with a lowest-order s-wave SU(3) chiral Lagrangian we study low-energy meson-baryon scattering in the strangeness $S=-2$ sector. A scattering-matrix pole is found around 1606 MeV which…
This is the first in a series of papers on scattering theory for one-dimensional Schr\"odinger operators with highly singular potentials $q\in H^{-1}(R)$. In this paper, we study Miura potentials $q$ associated to positive Schr\"odinger…
Probability of reflection $R(E)$ off a finite attractive scattering potential at zero or low energies is ordinarily supposed to be 1. However, a fully attractive potential presents a paradoxical result that $R(0)=0$ or $R(0)<1$, when an…
We consider discrete one-dimensional Schroedinger operators whose potentials decay asymptotically like an inverse square. In the super-critical case, where there are infinitely many discrete eigenvalues, we compute precise asymptotics of…
We study the quasi-periodic Schr\"odinger operator $$ -\psi"(x) + V(x) \psi(x) = E \psi(x), \qquad x \in \mathbb{R} $$ in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^\nu}c(m)\exp (2\pi i m\omega x)$, $\omega = (\omega_1, \dots,…
We determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of…
We provide a precise description of the bottom of the spectrum in the semiclassical limit of a harmonic-type Schr\"odinger operator with an inverse square potential. By exploiting the connection between the eigenfunctions of these operators…
We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from…
We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant magnetic field and electric potential V which typically decays at infinity exponentially fast or has a compact support. We investigate the asymptotic behaviour of…
We study the inverse spectral problem for periodic Schr\"odinger opera\-tors of kind $- \frac{1}{2} \hbar^2 \Delta_x + V(x)$ on the flat torus $\Bbb T^n := (\Bbb R / 2 \pi \Bbb Z)^n$ with potentials $V \in C^{\infty} (\Bbb T^n)$. We show…
In this paper the relativistic quantum dynamics of a spin-1/2 neutral particle with a magnetic moment $\mu$ in the cosmic string spacetime is reexamined by applying the von Neumann theory of self--adjoint extensions. Contrary to previous…
We consider the Schr\"odinger equation with a multipoint potential of Bethe-Peierls-Thomas-Fermi type. For this singular potential, we develop scattering and inverse scattering at high energies. In particular, in this framework, our results…
Let -Delta+V be the Schrodinger operator acting on L^2(R^d,C) with d>2 odd. Here V is a bounded real or complex function vanishing outside the closed ball of center 0 and of radius a. We show for generic potentials V that the number of…
We perform a semiclassical analysis for the planar Schr\"odinger-Poisson system \[ \cases{ -\varepsilon^{2} \Delta\psi+V(x)\psi= E(x) \psi \quad \text{in $\mathbb{R}^2$},\cr -\Delta E= |\psi|^{2} \quad \text{in $\mathbb{R}^2$}, \cr }…