On the adiabatic theorem when eigenvalues dive into the continuum

Decebal Horia Cornean, Arne Jensen, Hans Konrad Knörr, Gheorghe Nenciu

Research output: Working paperResearch


For a Wigner-Weisskopf model of an atom consisting of a quantum dot coupled to an energy reservoir described by a three-dimensional Laplacian 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.
Original languageEnglish
Number of pages21
Publication statusPublished - 8 Dec 2016
SeriesarXiv.org (e-prints)


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