A model of interband radiative transition

Jaroslav Dittrich, Pavel Exner, Masao Hirokawa

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)753-786
Number of pages34
JournalJournal of the Mathematical Society of Japan
Issue number3
Publication statusPublished - 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


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