On the adiabatic theorem when eigenvalues dive into the continuum
Abstract
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. At the end of the paper we present a short outlook on how our method may be extended to cover other classes of Hamiltonians; details will be given elsewhere.
Cite
@article{arxiv.1612.02354,
title = {On the adiabatic theorem when eigenvalues dive into the continuum},
author = {Horia D. Cornean and Arne Jensen and Hans Konrad Knörr and Gheorghe Nenciu},
journal= {arXiv preprint arXiv:1612.02354},
year = {2018}
}
Comments
22 pages, 1 figure