A model of interband radiative transition
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- Dittrich Jaroslav DITTRICH Jaroslav
- Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences
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- Exner Pavel EXNER Pavel
- Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences
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- Hirokawa Masao HIROKAWA Masao
- Department of Mathematics, Faculty of Science Okayama University
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Author(s)
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- Dittrich Jaroslav DITTRICH Jaroslav
- Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences
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- Exner Pavel EXNER Pavel
- Department of Theoretical Physics Nuclear Physics Institute Academy of Sciences
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- Hirokawa Masao HIROKAWA Masao
- Department of Mathematics, Faculty of Science Okayama University
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.
Journal
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 56(3), 753-786, 2004-07-01
The Mathematical Society of Japan
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