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International Journal of Theoretical Physics

Renormalized Spectrum of Quasiparticle in Two States, Strongly Interacting with Multi-Mode Polarization Phonons at T = 0K

N. V. Tkach, Julia O. Seti, Оxana Voitsekhivska, V. V. Hutiv

Published Feb 1, 2022• 0 citations
Publisher
DOI
10.1007/s10773-022-04991-5

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Within unitary transformed Hamiltonian of Fröhlich type, using the Green's functions method, exact renormalized energy spectrum of quasiparticle strongly interacting with two-mode polarization phonons is obtained at T=0 K in a model of the system with limited number of its initial states. Exact analytical expressions for the average number of phonons in ground state and in all satellite states of the system are presented. Their dependences on a magnitude of interaction between quasiparticle and both phonon modes are analyzed.
The theory of renormalized energy spectrum of a multi-level quasiparticle interacting with polarization phonons at T=0T=0T=0 K is developed within the Feynman-Pines diagram technique in a new approach. It permits a successive separation of multiplicative diagrams from non-multiplicative ones for all orders of mass operator, and their partial summing as well. The obtained mass operator is presented as a sum of branched chain fractions, which effectively take into account the multi-phonon processes. For the two-level quasiparticle it is shown that just the interlevel (non-diagonal) interaction with phonons fundamentally changes the properties of the spectrum. In the vicinity of all threshold energies, the quasi-equidistant phonon satellite bands (i.e., groups of energy levels) are formed. They correspond to the complexes of bound states of a quasi-particle with many phonons.
The theory of renormalized energy spectrum of localized quasi-particle interacting with polarization phonons at finite temperature is developed within the Feynman-Pines diagram technique.The created computer program effectively takes into account multi-phonon processes, exactly defining all diagrams of mass operator together with their analytical expressions in arbitrary order over the coupling constant.Now it is possible to separate the pole and non-pole mass operator terms and perform a partial summing of their main terms.The renormalized spectrum of the system is obtained within the solution of dispersion equation in the vicinity of the main state where the high-and low-energy complexes of bound states are observed.The properties of the spectrum are analyzed depending on the coupling constant and the temperature.