Exponential Estimates in Adiabatic Quantum Evolution
  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. 
A. Joye and C.-E. Pfister