1998/07/24 by Alain Joye, A. Joye, Joye, A. +3 · 1 citation
Mathematics · Physics and Astronomy · #Quantum Mechanics and Applications #Spectral Theory in Mathematical Physics #advanced mathematical theories #math-ph #math.MP #msc:82C10
paper · pdf · doi:10.48550/arxiv.math-ph/9807031
6 pages, To appear in: Proceedings of XIIth Int.Cong.Math.Phys. Brisbane, 1997
arxiv created 1998/07/24 · arxiv updated 2009/11/30
We review recent results concerning the exponential behaviour of transition probabilities across a gap in the adiabatic limit of the time-dependent Schrödinger 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.