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Smooth adiabatic evolutions with leaky power tails

J. E. Avron·A. Elgart
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Abstract

Adiabatic evolutions with a gap condition have, under a range of circumstances, exponentially small tails that describe the leaking out of the spectral subspace. Adiabatic evolutions without a gap condition do not seem to have this feature in general. This is a known fact for eigenvalue crossing. We show that this is also the case for eigenvalues at the threshold of the continuous spectrum by considering the Friedrichs model.

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J. E. Avron, A. Elgart. 1999-11-08. Smooth adiabatic evolutions with leaky power tails. https://doi.org/10.1088/0305-4470%2F32%2F50%2F102

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