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|14h - 15h
|Léo Morin (U. de Copenhague)
|Quantum tunnelling between radial magnetic wells
This talk is devoted to the spectral analysis of 2D Schrödinger operators with inhomogeneous magnetic field. When the magnetic field has two symmetric minima, each well generates an eigenvalue of same order. Then, we expect tunnelling to happen: the two smallest eigenvalues are exponentially close to each other in the semiclassical limit. We prove this result in the case of radially symmetric wells. Based on the Helffer-Sjöstrand theory, we obtain an elegant and short proof. Even though non-magnetic tunnelling is already very well understood, magnetic fields come with specific issues. In particular, this is the first tunnelling result between purely magnetic wells, and the non-radial situation is still challenging. Finally, we observe some new purely magnetic effect on the interaction between the wells.
|15h15 - 16h15
|Olivier Bourget (UC Chile)
|On localization regimes for kicked quantum systems
We will discuss the spectral properties of some periodically kicked quantum systems defined on the lattice. We focus our analysis on the existence of (dynamical) localization regimes for a class of random perturbations.