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...
Semiclassical limit and well-posedness of nonlinear Schrödinger-Poisson systems.
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 quantization of circular billiard in homogeneous magnetic field: Berry-Tabor approach.
Semiclassical scattering by the Coulomb potential
Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation
Semiclassical spectral estimates for Toeplitz operators
Let be a compact Kähler manifold with integral Kähler class and a holomorphic Hermitian line bundle whose curvature is the symplectic form of . Let be a Hamiltonian, and let be the Toeplitz operator with multiplier acting on the space . We obtain estimates on the eigenvalues and eigensections of as , in terms of the classical Hamilton flow of . We study in some detail the case when is an integral coadjoint orbit of a Lie group.
Semiclassical states of nonlinear Schrödinger equations with bounded potentials
Using some perturbation results in critical point theory, we prove that a class of nonlinear Schrödinger equations possesses semiclassical states that concentrate near the critical points of the potential .
Short waves through thin interfaces and 2-microlocal measures
Singular Bohr–Sommerfeld rules for 2D integrable systems
Spectral projection, residue of the scattering amplitude and Schrödinger group expansion for barrier-top resonances
We study the spectral projection associated to a barrier-top resonance for the semiclassical Schrödinger operator. First, we prove a resolvent estimate for complex energies close to such a resonance. Using that estimate and an explicit representation of the resonant states, we show that the spectral projection has a semiclassical expansion in integer powers of , and compute its leading term. We use this result to compute the residue of the scattering amplitude at such a resonance. Eventually, we...
Spectral theory of damped quantum chaotic systems
We investigate the spectral distribution of the damped wave equation on a compact Riemannian manifold, especially in the case of a metric of negative curvature, for which the geodesic flow is Anosov. The main application is to obtain conditions (in terms of the geodesic flow on and the damping function) for which the energy of the waves decays exponentially fast, at least for smooth enough initial data. We review various estimates for the high frequency spectrum in terms of dynamically defined...
Spectre de l'opérateur de Schrödinger magnétique avec symétrie d'ordre six
Stability and semiclassics in self-generated fields
We consider non-interacting particles subject to a fixed external potential and a self-generated magnetic field . The total energy includes the field energy and we minimize over all particle states and magnetic fields. In the case of spin-1/2 particles this minimization leads to the coupled Maxwell-Pauli system. The parameter tunes the coupling strength between the field and the particles and it effectively determines the strength of the field. We investigate the stability and the semiclassical...
Strichartz inequalities for Lipschitz metrics on manifolds and nonlinear Schrödinger equation on domains
We prove wellposedness of the Cauchy problem for the nonlinear Schrödinger equation for any defocusing power nonlinearity on a domain of the plane with Dirichlet boundary conditions. The main argument is based on a generalized Strichartz inequality on manifolds with Lipschitz metric.
Study of the behavior of quantum dynamics as
Sur le caractère bien posé des équations de Schrödinger non linéaires
Sur le spectre semi-classique d’un système intégrable de dimension 1 autour d’une singularité hyperbolique
Dans cette article on décrit le spectre semi-classique d’un opérateur de Schrödinger sur avec un potentiel type double puits. La description qu’on donne est celle du spectre autour du maximum local du potentiel. Dans la classification des singularités de l’application moment d’un système intégrable, le double puits représente le cas des singularités non-dégénérées de type hyperbolique.