arXiv subjects
Publications and source records attributed to Olivier Lablée.
In this article we consider a closed Riemannian manifold (M,g) and A a subset of M. The purpose of this article is the comparison between the eigenvalues of a Schrodinger operator on the manifold (M,g) and the eigenvalues on the manifold (M-A,g) with Dirichlet boundary conditions.
The paper deals with the semi-classical behaviour of quantum dynamics for a semi-classical completely integrable system with two degrees of freedom near Liouville regular torus. The phenomomenon of wave packet revivals is demonstrated in this article. The framework of this paper is semi-classical analysis (limit :). For the proofs we use standard tools of real analysis, Fourier analysis and basic analytic number theory.
The aim of this paper is to study the semi-classical behaviour of Schrödinger's dynamics for an one-dimesional quantum Hamiltonian with a classical hyperbolic trajectory. As in the regular case (elliptic trajectory), we prove, that for an initial wave packets localized in energy, the dynamics follows the classical motion during short time. And, for large time, a new period for the dynamics appears : the wave packets revivals.
In this article we give a panoramic view on semi-classical analysis.
In this article we describe the semi-classical spectrum of a Schrodinger operator on $\mathbb{R}$ with a double well potential. We study the shape of spectrum around the local maximum of the potential. In the classification of singularities of integrable systems, the double wells is the model of non-degenerate hyperbolic singularity.