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Within the unitary transformed Hamiltonian of Frohlich type, using the retarded Green’s function method, the exact renormalized energy spectrum of a quasi-particle strongly interacting with three-mode polarization phonons is obtained at T = 0 K in the model of a system with a limited number of its initial states. The exact analytical expressions for the average number of phonons in the main and all satellite states of the system are obtained. Their dependences on the magnitude of the interaction between quasi-particle and both phonon modes are analyzed.

Within unitary transformed Hamiltonian of Fr\"ohlich 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., Comment: 8 pages, 1 figure

The new method of calculation of a mass operator of Fourier image of Green's function, based at the generalized method of Feynman-Pines diagram technique for the multi-level systems, is proposed for the system of three-level localized quasiparticle interacting with polarization phonons at T=0K. The main class of diagrams, studied in this approach, made it possible to renormalize the mass operator and present it in a form of continuous branch chain fraction with typical chains. It allows effective accounting of multi-phonon processes. It is shown that the complicated complexes of bound-to-multi-phonons states of quasi-particle are observed in the energy spectrum of the system under research.

Using the model of rectangular potential and smooth position-dependent electron effective mass, which is a linear function of coordinate in near-interface regions between wells and barriers of open double-barrier resonant tunneling nano-structure, the solutions of Schrodinger equation are obtained and transmitting coefficient of the structure is analytically calculated. The influence of the sizes of inner and outer near-interface regions on transmitting coefficient of the structure is investigated. The comparative analysis of resonance energies and resonance widths of sub-barrier electron quasi-stationary states as functions of these sizes is performed. It is shown that the relative differences of resonance energies and resonance widths of the same state of electron in the model of linearly-dependent effective mass and simplified abrupt one do not exceed 1% and 5%, respectively, in physically correct interval of the sizes of outer and inner near-interface regions.

The spectrum of three-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 in such system, besides the renormalized three main states, the complexes of bound states exist. Their properties are essentially different depending on the energetic distance between the starting levels, which are in resonance with the phonon energy or not.

The resonance and non-resonance transmission canals of double-barrier resonant tunneling structure are established for the electron photon system using the exact solution of one-dimensional non-stationary Schrodinger equation expanded into the Fourier range. It is shown that besides the main and satellite, the mixed quasi-stationary states which cause the appearance of speci c transmission canals with the properties strongly dependent on the intensity and frequency of electromagnetic eld, exist in the nanostructure.

The theory of resonance energies and widths of electron quasi-stationary states and electronic conductivity in open cylindrical two-barrier symmetric resonance tunnel structure is developed. The complete Schrodinger equation is solved within the model of effective masses for rectangular potential wells and barriers. Interaction between electrons and electromagnetic field was taken into account using the approximation of the small signal. The calculations of spectral parameters are performed for In0.53Ga0.47As/In0.52Al0.48As resonance tunnel structure. The dependences of conductivity on the energy of mono-energy electrons beam falling at the system and electromagnetic field energy absorbed or emitted by the system are obtained and analyzed. The relation between experimentally measured parameters of conductivity and resonance widths of electron quasi-stationary states in open resonance tunnel structure is established.

Partial summing of infinite range of diagrams for the two-phonon mass operator of polaron described by Fr\"{o}hlich Hamiltonian is performed using the Feynman-Pines diagram technique. Renormalized spectral parameters of ground and first excited (phonon repeat) polaron state are accurately calculated for a weak electron-phonon coupling at $T=0$ K. It is shown that the stronger electron-phonon interaction shifts the energy of both states into low-energy region of the spectra. The ground state stays stationary and the excited one decays at a bigger coupling constant., Comment: 12 pages, 5 figures

The spectral characteristics of exciton in combined nanoheterosystem consisting of semiconductor cylindrical quantum wire containing two quantum dots separated by thin barrier-shell are investigated. It is shown that the binding energy non monotonously depends on the geometrical characteristics of nanoheterosystem approaching several minimum and maximum magnitudes.

The theory of exciton spectrum in spherically symmetric states for the three- shell closed spherical quantum dot is proposed. The evolution of the exciton spectrum while varying the outer well thickness from zero (stationary spectrum of single closed spherical quantum dot) to infinity (quasistationary spectrum of a single open spherical quantum dot) is investigated. The mechanism of damping (semiwidth) of quasistationary states due to the redistribution over the energy levels of probability of exciton location in the space of two inner shells of nanosystem is studied. It is shown that the three shell closed spherical quantum dot of a rather big thickness of the outer well quite sufficiently and exactly reflects the basic properties of the quasistationary exciton spectrum in a single open spherical quantum dot. Вперше запропонована теорiя екситонного спектра в сферично-симетричних станах тришарової закритої сферичної квантової точки (СКТ). Дослiджено еволюцiю спектра при змiнi товщини зовнiшнього шару-ями вiд нуля (стацiонарний спектр простої закритої СКТ) до безмежностi (квазiстацiонарний спектр простої вiдкритої СКТ). Дослiджено механiзм виникнення затухання (пiвширини) квазiстацiонарних станiв причиною якого є перерозподiл по енергетичних рiвнях ймовiрностей перебування екситона у межах двох внутрiшнiх шарiв наносистеми. Показано, що тришарова закрита СКТ з достатньо великою товщиною зовнiшньої ями з довiльною необхiдною точнiстю вiдтворює основнi властивостi квазiстацiонарного екситонного спектра у простiй вiдкритiй СКТ.

Within the model of rectangular potentials and different effective masses of electrons in different elements of plane two-barrier resonance tunnel structure there is developed a theory of spectral parameters of quasi-stationary states and active conductivity for the case of mono-energetic electronic current interacting with electromagnetic field. It is shown that the two-barrier resonance tunnel structure can be utilized as a separate or active element of quantum cascade laser or detector. For the experimentally studied In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As nano-system it is established that the two-barrier resonance tunnel structure, in detector and laser regimes, optimally operates (with the biggest conductivity at the smallest exciting current) at the quantum transitions between the lowest quasi-stationary states., 11 pages, 4 figures