Exponential Estimates in Adiabatic Quantum Evolution

Abstract

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.

6 pages, To appear in: Proceedings of XIIth Int.Cong.Math.Phys. Brisbane, 1997

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