Related papers: Semi-classical analysis of Schrodinger operators a…
We show that the behaviour of analytic eigenbranches of a Schr\"odinger operator depends on the way eigenfunctions concentrate in the phase space.
We present an overview over recent results concerning semi-classical spectral estimates for magnetic Schroedinger operators. We discuss how the constants in magnetic and non-magnetic eigenvalue bounds are related and we prove, in an…
This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magnetic field is positive and a few generic conditions, we…
We discuss compactness of the d-bar-Neumann operator in the setting of weighted L^2-spaces on C^n.$ For this purpose we use a description of relatively compact subsets of L^2- spaces. We also point out how to use this method to show that…
In this paper we characterize compactness of the canonical solution operator to d-bar on weigthed $L^2$ spaces on $\mathbb C.$ For this purpose we consider certain Schr\"odinger operators with magnetic fields and use a condition which is…
This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L^2-space). For perturbations by a (nonnegative)…
We consider a Schr\"odinger operator with a Hermitian 2x2 matrix-valued potential which is lattice periodic and can be diagonalized smoothly on the whole $R^n.$ In the case of potential taking its minimum only on the lattice, we prove that…
We study the Schroedinger operator with a constant magnetic field in the exterior of a two-dimensional compact domain. Functions in the domain of the operator are subject to a boundary condition of the third type (Robin condition). In…
Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schr\"odinger operator with a purely imaginary potential $h^2\Delta+iV$ in the semiclassical limit $h\to 0$ we…
We study the asymptotic behavior as |x| \to \infty of Schr\"odinger operators with homogeneous potentials. For this purpose, we use methods from semiclassical analysis and investigate semiclassical defect mesures. We prove their…
The semiclassical limit of the derivative nonlinear Schrodinger equation with periodic initial conditions is studied analytically and numerically. The spectrum of the associated scattering problem for a certain class of initial conditions,…
We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schr\"odinger operator with magnetic wells on a noncompact Riemannian manifold $M$ such that $H^1(M, \R)=0$ equipped with a properly…
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…
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…
In this paper, we study the semiclassical limit for the stationary magnetic nonlinear Schr\"odinger equation \begin{align}\label{eq:initialabstract}\left( i \hbar \nabla + A(x) \right)^2 u + V(x) u = |u|^{p-2} u, \quad x\in…
We study the quasi-classical limit of the Pauli-Fierz model: the system is composed of finitely many non-relativistic charged particles interacting with a bosonic radiation field. We trace out the degrees of freedom of the field, and…
We consider the semi-classical Dirichlet Pauli operator in bounded connected domains in the plane. Rather optimal results have been obtained in previous papers by Ekholm-Kova\v{r}\'ik-Portmann and Helffer-Sundqvist for the asymptotics of…
The asymptotic behavior of the first eigenvalues of magnetic Laplacian operators with large magnetic fields and Neumann realization in polyhedral domains is characterized by a hierarchy of model problems. We investigate properties of the…
We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…
In this paper we characterize compactness of the canonical solution operator to d-bar on weighted L^2 spaces on C. For this purpose we consider certain Schr\"odinger operators with magnetic fields and use a condition which is equivalent to…