Magnetic barriers of compact support and eigenvalues in spectral gaps.
Mathematical transform of traveling-wave equations and phase aspects of quantum interaction.
Matrices de diffusion pour l'opérateur de Schrödinger avec champ magnétique et phénomène de Aharonov-Bohm
Matrices de diffusion pour l'opérateur de Schrödinger en présence d'un champ magnétique. Phénomène de Aharonov-Bohm
Maxwell-Schrödinger equations in singular electromagnetic field
We investigate the Cauchy problem of the one dimensional Maxwell-Schrödinger (MS) system under the Lorenz gauge condition. Different from the classical case, we consider the electromagnetic and electrostatic potentials which are growing at space infinity. More precisely, the electrostatic potential is allowed to grow linearly, while for the electromagnetic potential the growth is sublinear. Based on the energy estimates and the gauge transformation, we prove the global existence and the uniqueness...
Mean-field evolution of fermionic systems
We study the dynamics of interacting fermionic systems, in the mean-field regime. We consider initial states which are close to quasi-free states and prove that, under suitable assumptions on the inital data and on the many-body interaction, the quantum evolution of the system is approximated by a time-dependent quasi-free state. In particular we prove that the evolution of the reduced one-particle density matrix converges, as the number of particles goes to infinity, to the solution of the time-dependent...
Mesures semi-classiques et croisement de modes
L’étude de la dynamique semi-classique d’électrons dans un cristal débouche naturellement sur le problème de l’évolution des mesures semi-classiques en présence d’un croisement de modes. Dans ce travail, nous étudions un système qui présente un tel croisement. À cet effet, nous introduisons des mesures semi-classiques à deux échelles qui décrivent comment la transformée de Wigner usuelle se concentre sur l’ensemble des trajectoires rencontrant ce croisement. Puis nous établissons des formules...
Modulation space estimates for Schrödinger type equations with time-dependent potentials
We give a new representation of solutions to a class of time-dependent Schrödinger type equations via the short-time Fourier transform and the method of characteristics. Moreover, we also establish some novel estimates for oscillatory integrals which are associated with the fractional power of negative Laplacian with . Consequently the classical Hamiltonian corresponding to the previous Schrödinger type equations is studied. As applications, a series of new boundedness results for the corresponding...