Joye A., Pfister C.-E.
Exponential Estimates in Adiabatic Quantum Evolution.
(25K, LATeX)

ABSTRACT.  We review recent results concerning the exponential 
behaviour of transition probabilities across a gap in the adiabatic 
limit of the time-dependent Schr\"odinger equation. They range 
from an exponential estimate in quite general situations to 
asymptotic Landau-Zener type formulae for finite dimensional 
systems, or systems reducible to this case.