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 B ogolubov transformation diagonalizing the total Hamiltonian is constructed. It is pointed out that the transformation is improper when the discrete pa rt 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 t he bare vacuum and the bare operators is calculated. Using the exact soluti on, the result of Passante, Petrosky, and Prigogine [Physica A 218, 437 (19 95)] that the transition from the bare vacuum state to the true vacuum lead s to the emission of real photons is confirmed. The dressing of the bare va cuum at the presence of resonances is an irreversible process. The relation of the result with the idea of "indirect spectroscopy" is discussed. (C) 2 000 American Institute of Physics. [S0022-2488(00)02701-8].