A Stationary Schrödinger-Poisson System Arising from the Modelling of Electronic Devices.
Formulation variationnelle de systèmes Schrödinger-Poisson en dimension
A semi-classical picture of quantum scattering
Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach.
We present here a simplified version of recent results obtained with B. Helffer and M. Klein. They are concerned with the exponentally small eigenvalues of the Witten Laplacian on -forms. We show how the Witten complex structure is better taken into account by working with singular values. This provides a convenient framework to derive accurate approximations of the first eigenvalues of and solves efficiently the question of weakly resonant wells.
Quelques critères pour l’inégalité de Poincaré dans ,
Remarques sur les algorithmes de décomposition de domaines
À propos des fonctions thêta et des réseaux d’Abrikosov
Une approche alternative de l’évolution adiabatique des résonances de forme 1D .
Adiabatic approximation for a two-level atom in a light beam
Following the recent experimental realization of synthetic gauge potentials, Jean Dalibard addressed the question whether the adiabatic ansatz could be mathematically justified for a model of an atom in 2 internal states, shone by a quasi resonant laser beam. In this paper, we derive rigorously the asymptotic model guessed by the physicists, and show that this asymptotic analysis contains the information about the presence of vortices. Surprisingly, the main difficulties do not come from the nonlinear...
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