J. E. Avron, A. Elgart
Smooth adiabatic evolutions with leaky power tails
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ABSTRACT.  Adiabatic evolutions with a gap condition have, under a 
range of circumstances, exponentially small tails that describe 
the leaking out of the spectral subspace. Adiabatic evolutions 
without a gap condition do not seem to have this feature in 
general. 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.