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Hans- Konrad Knörr

On the adiabatic theorem when eigenvalues dive into the continuum

Abstract: We consider a Wigner-Weisskopf model of an atom consisting of a zero-dimensional quantum dot coupled to an absolutely continuous energy reservoir described by a 3D Laplacian. For this model we study 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.

This talk is based on joint work with H. Cornean, A. Jensen and G. Nenciu.