Abstract
We study an adiabatic invariant for the time-dependent Schrödinger equation which gives the transition probability across a gap from timet′ to timet. When the hamiltonian depends analytically on time, andt′=−∞,t=+∞ we give sufficient conditions so that this adiabatic invariant tends to zero exponentially fast in the adiabatic limit.
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Communicated by J. Fröhlich
Supported by Fonds National Suisse de la Recherche, Grant 2000-5.600
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Joye, A., Pfister, CE. Exponentially small adiabatic invariant for the Schrödinger equation. Commun.Math. Phys. 140, 15–41 (1991). https://doi.org/10.1007/BF02099288
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DOI: https://doi.org/10.1007/BF02099288