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A model of interband radiative transitions

J. Dittrich·P. Exner·M. Hirokawa
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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 curve-type singularity in the lower halfplane which is a deformation of the upper-band 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 power-like behaviour.

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J. Dittrich, P. Exner, M. Hirokawa. 2000-11-07. A model of interband radiative transitions. https://arxiv.org/abs/math-ph/0011009

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