 00442 Dittrich J., Exner P., Hirokawa M.
 A model of interband radiative transition
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Nov 9, 00

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Abstract. We consider a simple model which is a caricature of a crystal interacting with a radiation field. The model has two bands of continuous spectrum and the particle can pass from the upper one to the lower by radiating a photon, the coupling between the excited and deexcited states being of a Friedrichs type. Under suitable regularity and analyticity assumptions we find the continued resolvent and show that for weak enough coupling it has a curvetype singularity in the lower halfplane which is a deformation of the upperband spectral cut. We then find a formula for the decay amplitude and show that for a fixed energy it is approximately exponential at intermediate times, while the tail has a powerlike behaviour.
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