Open Access
July, 2004 A model of interband radiative transition
J. Math. Soc. Japan 56(3): 753-786 (July, 2004). DOI: 10.2969/jmsj/1191334085


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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Jaroslav DITTRICH. Pavel EXNER. Masao HIROKAWA. "A model of interband radiative transition." J. Math. Soc. Japan 56 (3) 753 - 786, July, 2004.


Published: July, 2004
First available in Project Euclid: 2 October 2007

zbMATH: 1059.81196
MathSciNet: MR2071672
Digital Object Identifier: 10.2969/jmsj/1191334085

Primary: 81Q15
Secondary: 81V10

Keywords: crystal spectral band , decay law , Friedrichs model , Radiative transition

Rights: Copyright © 2004 Mathematical Society of Japan

Vol.56 • No. 3 • July, 2004
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