Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. In general, adiabatic evolutions without a gap condition do not seem to have this feature. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy (all)