A model of interband radiative transitions
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.
 Publication:

arXiv eprints
 Pub Date:
 November 2000
 arXiv:
 arXiv:mathph/0011009
 Bibcode:
 2000math.ph..11009D
 Keywords:

 Mathematical Physics;
 Condensed Matter;
 Mathematics  Dynamical Systems;
 Quantum Physics;
 81Q05
 EPrint:
 42 pages