A model of interband radiative transition

Jaroslav Dittrich, Pavel Exner, Masao Hirokawa

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)753-786
Number of pages34
JournalJournal of the Mathematical Society of Japan
Volume56
Issue number3
DOIs
Publication statusPublished - Jan 1 2004
Externally publishedYes

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Continuous Spectrum
Weak Coupling
Analyticity
Resolvent
Half-plane
Tail
Photon
Crystal
Regularity
Radiation
Singularity
Decay
Curve
Energy
Model

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

A model of interband radiative transition. / Dittrich, Jaroslav; Exner, Pavel; Hirokawa, Masao.

In: Journal of the Mathematical Society of Japan, Vol. 56, No. 3, 01.01.2004, p. 753-786.

Research output: Contribution to journalArticle

Dittrich, Jaroslav ; Exner, Pavel ; Hirokawa, Masao. / A model of interband radiative transition. In: Journal of the Mathematical Society of Japan. 2004 ; Vol. 56, No. 3. pp. 753-786.
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