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

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Abstract

Within unitary transformed Hamiltonian of Frohlich type, the exact renormalized energy spectrum of a system consisting of a two-state quasiparticle strongly interacting with multi-mode polarization phonons at T = 0K is obtained using the method of retarded Green’s functions. The exact analytical expressions for the average numbers of phonons in the main and all satellite states of the system are presented. It is shown that renormalized spectrum of the system is stationary and discrete, regardless of the number of phonon modes (τ). It contains the main level and (2τ − 1) groups of an infinite number of satellite levels corresponding to the complexes of strongly bound quasiparticle with all phonons of all possible combinations of modes. The main and first satellite levels are non-degenerate and the rest of the satellite part of the spectrum depends significantly on the ratios between the energies of the phonon modes. If the energies of all modes are multiples of the smallest one, then the spectrum is equidistant and degenerate. If at least one of the modes is not a multiple of the other, and the others are multiples of each other, then the spectrum is not equidistant and partially degenerate. If the ratios are irrational numbers, then the spectrum is neither degenerate nor equidistant.

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The work is performed under Phyton 3 by using the code which is written by co-authors of the paper.

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Authors and Affiliations

  1. Department of Theoretical Physics and Computer Simulation, Yuriy Fedkovych Chernivtsi National University, Kotsyubinsky Str., Chernivtsi, 58012, Ukraine

    Mykola Tkach, Julia Seti, Oxana Voitsekhivska & Vasyl Hutiv

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  1. Mykola Tkach
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  2. Julia Seti
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  3. Oxana Voitsekhivska
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Contributions

Analytical and numerical calculations, creation of the computer code, data collection, preparation of graphic results and analysis were performed by Mykola Tkach, Julia Seti, Oxana Voitsekhivska and Vasyl Hutiv. The first draft of the manuscript was written by Mykola Tkach and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Mykola Tkach.

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Julia Seti, Oxana Voitsekhivska and Vasyl Hutiv contributed equally to this work.

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Tkach, M., Seti, J., Voitsekhivska, O. et al. Renormalized Spectrum of Quasiparticle in Two States, Strongly Interacting with Multi-Mode Polarization Phonons at T = 0K. Int J Theor Phys 61, 29 (2022). https://doi.org/10.1007/s10773-022-04991-5

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