Friedrichs model with virtual transitions. Exact solution and indirect spectroscopy

The Friedrichs-type model of interaction between matter (multilevel system) and radiation including virtual transitions is considered. The canonical Bogolubov transformation diagonalizing the total Hamiltonian is constructed. It is pointed out that the transformation is improper when the discrete pa...

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Veröffentlicht in:Journal of mathematical physics 2000-01, Vol.41 (1), p.118-131
Hauptverfasser: Karpov, E., Prigogine, I., Petrosky, T., Pronko, G.
Format: Artikel
Sprache:eng
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Zusammenfassung:The Friedrichs-type model of interaction between matter (multilevel system) and radiation including virtual transitions is considered. The canonical Bogolubov transformation diagonalizing the total Hamiltonian is constructed. It is pointed out that the transformation is improper when the discrete part of the spectrum of system is “dissolved” in the continuous one. The new vacuum state for the total Hamiltonian is obtained. The time evolution of the bare vacuum and the bare operators is calculated. Using the exact solution, the result of Passante, Petrosky, and Prigogine [Physica A 218, 437 (1995)] that the transition from the bare vacuum state to the true vacuum leads to the emission of real photons is confirmed. The dressing of the bare vacuum at the presence of resonances is an irreversible process. The relation of the result with the idea of “indirect spectroscopy” is discussed.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.533125