Exponential Estimates in Adiabatic Quantum Evolution

Details Exponential Estimates in Adiabatic Quantum Evolution Exponential Estimates in Adiabatic Quantum Evolution

1998-07-24

arxiv.org/abs/math-ph/9807031v1

Physics

Mathematical Physics

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

Scientific paper

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.

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