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Horia Cornean

On the adiabatic theorem when eigenvalues dive into the continuum
星期一, 5 三月, 2018 - 13:30
Résumé : 

We consider a reduced two-channel model of an atom consisting of a quantum dot coupled to an open scattering channel described by a three-dimensional Laplacian. We are interested in the survival probability of a bound state when the dot energy varies smoothly and adiabatically in time. The initial state corresponds to a discrete eigenvalue which dives into the continuous spectrum and re-emerges from it as the dot energy is varied in time and finally returns to its initial value. Our main result is that for a large class of couplings, the survival probability of this bound state vanishes in the adiabatic limit. We shall also explain why our method is expected to work for other classes of Hamiltonians. This is joint work with A. Jensen, H.K. Knorr, and G. Nenciu.

Institution de l'orateur : 
Aalborg University
Thème de recherche : 
Physique mathématique
Salle : 
Salle 1, tour IRMA
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