Abstract
Using the Feynman-Pines diagram technique, the energy spectrum of localized quasi-particles interacting with polarization phonons is calculated and analyzed in the wide range of energies at the finite temperature of the system. It is established that the general model of the system, besides the bound states known from the simplified model with an additional condition for the operator of quasi-particles number, contains the new bound states even for the systems with weak coupling. The contribution of multi-phonon processes into the formation of renormalized spectrum of the system is analyzed. The reasons of the appearance, behaviour and disappearance of separate pairs of bound states depending on the coupling constant and temperature are revealed.
Highlights
The theory of the renormalized energy spectrum of a system of quasi-particles interacting with phonons in a wide range of energies and coupling constants has been attracting a permanent attention [1, 2]
We obtain a renormalized spectrum of localized quasi-particles interacting with polarization phonons using the general model for systems with weak coupling at a finite temperature
Taking into account the analysis of the properties of the spectra and average numbers of phonons in the “coats” of localized quasi-particles interacting with polarization phonons we can conclude that the results of the exact model (a) according to their main features are the same as the results of model (b) in which all unmixed scattering processes are considered
Summary
The theory of the renormalized energy spectrum of a system of quasi-particles interacting with phonons in a wide range of energies (containing bound states) and coupling constants has been attracting a permanent attention [1, 2]. We obtain a renormalized spectrum of localized quasi-particles interacting with polarization phonons using the general model (without the above mentioned additional condition) for systems with weak coupling at a finite temperature.
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