Scattering phases and density of states for exterior domains
Schrödinger operator with magnetic field in domain with corners
We present here a simplified version of results obtained with F. Alouges, M. Dauge, B. Helffer and G. Vial (cf [4, 7, 9]). We analyze the Schrödinger operator with magnetic field in an infinite sector. This study allows to determine accurate approximation of the low-lying eigenpairs of the Schrödinger operator in domains with corners. We complete this analysis with numerical experiments.
Self-adjointness of Schrödinger-type operators with singular potentials on manifolds of bounded geometry.
Self-similar solutions for nonlinear Schrödinger equations.
Semiclassical analysis of low lying eigenvalues. I. Non degenerate minima : asymptotic expansions
Semiclassical analysis of low lying eigenvalues. I. Non-degenerate minima : asymptotic expansions
Semiclassical and weak-magnetic-field eigenvalue asymptotics for the Schrödinger operator with electromagnetic potential
Semi-classical approximation and microcanonical ensemble
Semiclassical asymptotics for exchange energy
Semi-classical eigenstates at the bottom of a multidimensional well
Semiclassical expansion for the thermodynamic limit of the ground state energy of Kac's operator
We continue the study started by the first author of the semiclassical Kac Operator. This kind of operator has been obtained for example by M. Kac as he was studying a 2D spin lattice by the so-called “transfer operator method”. We are interested here in the thermodynamical limit of the ground state energy of this operator. For Kac’s spin model, is the free energy per spin, and the semiclassical regime corresponds to the mean-field approximation. Under suitable assumptions, which are satisfied...
Semi-classical formula beyond the Ehrenfest time in quantum chaos. (I) Trace formula
We consider a nonlinear area preserving Anosov map on the torus phase space, which is the simplest example of a fully chaotic dynamics. We are interested in the quantum dynamics for long time, generated by the unitary quantum propagator . The usual semi-classical Trace formula expresses for finite time , in the limit , in terms of periodic orbits of of period . Recent work reach time where is the Ehrenfest time, and is the Lyapounov coefficient. Using a semi-classical normal form...
Semiclassical limit and well-posedness of nonlinear Schrödinger-Poisson systems.
Semiclassical limit for perturbations of non-resonant rotators
Semiclassical Limit of the cubic nonlinear Schrödinger Equation concerning a superfluid passing an obstacle
In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches
Semiclassical limit of the spectral decomposition of a Schrödinger operator in one dimension.
Semiclassical measures for the Schrödinger equation on the torus
In this article, the structure of semiclassical measures for solutions to the linear Schrödinger equation on the torus is analysed. We show that the disintegration of such a measure on every invariant lagrangian torus is absolutely continuous with respect to the Lebesgue measure. We obtain an expression of the Radon-Nikodym derivative in terms of the sequence of initial data and show that it satisfies an explicit propagation law. As a consequence, we also prove an observability inequality, saying...
Semiclassical quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach.
Semiclassical Resonances and trace formulae for non-semi-bounded Hamiltonians
Semiclassical scattering by the Coulomb potential