Abstract
The spectrum of two-level localized quasi-particle renormalized due to the interaction with polarization phonons is studied within the Feynman-pines diagram technique at cryogenic temperature. It is shown that when the energy distance between the both main states varies, the renormalized spectrum of the energies contains two series of levels corresponding to the both main and their excited states which appear due to the interaction with phonons. The quasi-equidistant spectrum is observed in the non-resonance regions of energies while in the resonance regions the anti-crossing effect is seen.
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