A model of interband radiative transition
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.
Permanent link to this document: http://projecteuclid.org/euclid.jmsj/1191334085
Digital Object Identifier: doi:10.2969/jmsj/1191334085
Mathematical Reviews number (MathSciNet): MR2071672
Zentralblatt MATH identifier: 1059.81196