Étude semi-classique d'observables quantiques
Hamiltonian identification for quantum systems: well-posedness and numerical approaches
This paper considers the inversion problem related to the manipulation of quantum systems using laser-matter interactions. The focus is on the identification of the field free Hamiltonian and/or the dipole moment of a quantum system. The evolution of the system is given by the Schrödinger equation. The available data are observations as a function of time corresponding to dynamics generated by electric fields. The well-posedness of the problem is proved, mainly focusing on the uniqueness of the...
High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials
Illustration of the quantum central limit theorem by independent addition of spins
Limitations on the control of Schrödinger equations
We give the definitions of exact and approximate controllability for linear and nonlinear Schrödinger equations, review fundamental criteria for controllability and revisit a classical “No-go” result for evolution equations due to Ball, Marsden and Slemrod. In Section 2 we prove corresponding results on non-controllability for the linear Schrödinger equation and distributed additive control, and we show that the Hartree equation of quantum chemistry with bilinear control is not controllable...
Limite semi-classique de l'amplitude de diffusion
Maximum entropy wave functions.
New method to solve certain differential equations
A new method to solve stationary one-dimensional Schroedinger equation is investigated. Solutions are described by means of representation of circles with multiple winding number. The results are demonstrated using the well-known analytical solutions of the Schroedinger equation.
Nonlinear Dirac equations.
On orthogonality relations for dual discrete -ultraspherical polynomials.
On recurrence relations for radial wave functions for the -th dimensional oscillators and hydrogenlike atoms: analytical and numerical study.
On some spaces of linear functionals on the algebras for locally compact groups
Quantification et analyse pseudo-différentielle
Quantizations and symbolic calculus over the -adic numbers
We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the -adic numbers. We apply this theory to the study of elliptic operators over the -adic numbers and determine their asymptotic spectral behavior.
Quantum detailed balance
Quantum fluctuations of elementary excitations in discrete media.
Quantum mechanics in strong time dependent external fields
Quasi-covariant repesentations of nuclear ...-algebras
Résonances multiples en limite semi-classique
Semiclassical limit for perturbations of non-resonant rotators