Related papers: Semiclassical resonances for a two-level Schr\"odi…
We study the semiclassical distribution of resonances of a $2 \times 2$ matrix Schr\"odinger operator, obtained as a reduction of an Hamiltonian when studying molecular predissociation models under the Born-Oppenheimer approximation. The…
We study the existence and location of the resonances of a $2\times 2$ semiclassical system of coupled Schr\"odinger operators, in the case where the two electronic levels cross at some point, and one of them is bonding, while the other one…
We study the resonances of a two-by-two semiclassical system of one dimensional Schr\"odinger operators, near an energy where the two potentials intersect transversally, one of them being bonding, and the other one anti-bonding. Under an…
This paper is concerned with the asymptotics of resonances in the semiclassical limit $h\to 0^+$ for $2\times 2$ matrix Schr\"odinger operators in one dimension. We study the case where the two underlying classical Hamiltonian trajectories…
We investigate the existence of resonances for two-centers Coulomb systems with arbitrary charges in two dimensions, defining them in terms of generalised complex eigenvalues of a non-selfadjoint deformation of the two-centers Schr\"odinger…
We consider a 1D $2\times 2$ matrix-valued operator \eqref{System0} with two semiclassical Schr\"odinger operators on the diagonal entries and small interactions on the off-diagonal ones. When the two potentials cross at a turning point…
We prove that the spectrum of certain non-self-adjoint Schrodinger operators is unstable in the semi-classical limit. Similar results hold for a fixed operator in the high energy limit. The method involves the construction of approximate…
We review an "exact semiclassical" resolution method for the general stationary 1D Schr\"odinger equation with a polynomial potential. This method avoids having to compute any Stokes phenomena directly; instead, it basically relies on an…
A concept of semiclassically concentrated solutions is formulated for the multidimensional nonlinear Schr\"odinger equation (NLSE) with an external field. These solutions are considered as multidimensional solitary waves. The center of mass…
In this article we study the semiclassical spectral measures associated with Schr\"odinger operators on $R^n$. In particular we compute the first few coefficients of the asymptotic expansions of these measures and, as an application, give…
This paper is concerned with the efficient numerical computation of solutions to the 1D stationary Schr\"odinger equation in the semiclassical limit in the highly oscillatory regime. A previous approach to this problem based on explicitly…
The concept of near resonances for harmonic approximations of semiclassical Schr\"odinger operators is introduced and explored. Combined with a natural extension of the Birkhoff-Gustavson normal form, we obtain formulas for approaching the…
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…
Schr\"odinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to…
We study the asymptotic behavior of the Schr\"odinger equation in the presence of a nonlinearity of Hartree type in the semi-classical regime. Our scaling corresponds to a weakly nonlinear regime where the nonlinearity affects the leading…
We discuss a generalized Schr\"odinger operator in $L^2(\mathbb{R}^d), d=2,3$, with an attractive singular interaction supported by a $(d-1)$-dimensional hyperplane and a finite family of points. It can be regarded as a model of a leaky…
The three-wave resonant interaction equations are a non-dispersive system of partial differential equations with quadratic coupling describing the time evolution of the complex amplitudes of three resonant wave modes. Collisions of wave…
In this paper we examine the semiclassical behavior of the scattering data of a non-self-adjoint Dirac operator with a rapidly oscillating potential that is complex analytic in some neighborhood of the real line. Some of our results are…
We consider the semi-classical limit of nonlinear Schrodinger equations in the presence of both a polynomial nonlinearity and thederivative in space of a polynomial nonlinearity. By working in a class of analytic initial data, we do not…
In our recent papers, we studied semiclassical spectral problems for the Bochner-Schr\"odinger operator on a manifold of bounded geometry. We survey some results of these papers in the setting of the magnetic Schr\"odinger operator in the…