Properties of main and satellite states of two-level localized quasiparticles interacting with polarization phonons in nanostructures

In the framework of the Feynman–Pines diagram technique, the renormalized spectrum of two-level quasiparticle weakly interacting with phonons, being a model of the electron-phonon system in nanostructures, is calculated and analyzed. It is shown that the spectrum of the system contains the main quasiparticle states and complexes of bound-to-phonons satellite ones. These states form the bands. Their widths are proportional to the magnitudes of the constants of intralevel interactions. In the spectra where the energy difference between the main states of the quasiparticle is a multiple of the phonon energy, the anti-crossings, caused by interlevel interaction, occur.