ADVANCED COMPUTING TOPOLOGICAL AND DYNAMICAL INVARIANTS OF RELATIVISTIC BACKWARD-WAVE TUBE TIME SERIES IN CHAOTIC AND HYPERCHAOTIC REGIMES

The advanced results of computing the dynamical and topological invariants (correlation dimensions values, embedding, Kaplan-York dimensions, Lyapunov’s exponents, Kolmogorov entropy etc) of the dynamics time series of the relativistic backward-wave tube with accounting for dissipation and space charge field and other effects are presented for chaotic and hyperchaotic regimes. It is solved a system of equations for unidimensional relativistic electron phase and field unidimensional complex amplitude. The data obtained make more exact earlier presented preliminary data for dynamical and topological invariants of the relativistic backward-wave tube dynamics in chaotic regimes and allow to describe a scenario of transition to chaos in temporal dynamics.

OPTIMIZED QUASIPARTICLE DENSITY FUNCTIONAL APPROACH FOR MULTIELECTRON ATOMIC SYSTEMS

We present the optimized version of the quasiparticle density functional theory (DFT), constructed on the principles of the Landau-Migdal Fermi-liquids theory and principles of the optimized one-quasiparticle representation in theory of multielectron systems. The master equations can be naturally obtained on the basis of variational principle, starting from a Lagrangian of an atomic system as a functional of three quasiparticle densities. These densities are similar to the Hartree-Fock (HF) electron density and kinetical energy density correspondingly, however the third density has no an analog in the Hartree-Fock or the standard DFT theory and appears as result of account for the energy dependence of the mass operator S. The elaborated approach to construction of the eigen-functions basis can be characterized as an improved one in comparison with similar basises of other one-particle representations, namely, in the HF, the standard Kohn-Sham approximations etc.

THEORETICAL STUDYING EXCITED STATES SPECTRUM OF THE YTTERBIUM WITHIN THE OPTIMIZED RELATIVISTIC MANY-BODY PERTURBATION THEORY

Theoretical studying spectrum of the excited states for the ytterbium atom is carried out within the relativistic many-body perturbation theory with ab initio zeroth approximation and generalized relativistic energy approach. The zeroth approximation of the relativistic perturbation theory is provided by the optimized Dirac-Kohn-Sham ones. Optimization has been fulfilled by means of introduction of the parameter to the Kohn-Sham exchange potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian. The obtained theoretical data on energies E and widths W of the ytterbium excited states are compared with alternative theoretical results (the Dirac-Fock, relativistic Hartree-Fock, perturbation theories) and available experimental data. Analysis shows that the theoretical and experimental values ​​of energies are in good agreement with each other, however, the values ​​of widths differ significantly. In our opinion, this fact is explained by insufficiently accurate estimates of the radial integrals, the use of unoptimized bases, and some other approximations of the calculation.

METHODOLOGY OF CONVERTING OF THE COORDINATES OF THE BASIS ATOMS IN A UNIT CELL OF CRYSTALLINE Β-GA2O3, SPECIFIED IN A MONOCLINIC CRYSTALLOGRAPHIC SYSTEM, IN THE LABORATORY CARTESIAN COORDINATES FOR COMPUTER APPLICATIONS

One of the most important areas of modern technology is the creation of new structural materials with predetermined properties. Along with industrial methods for their preparation and technologies associated with the artificial growth of crystalline structures, various methods of computer modeling of new materials have recently become increasingly important. Such approaches can significantly reduce the number of full-scale experiments. Many applications of the computational materials science are related to the need to establish a relationship between structure and electronic characteristics, and other physical properties of crystals. This article on the example of crystalline β-Ga2O3 presents the algorithms used in the converting of the coordinates of the basis atoms in a unit cell of crystal, specified in a crystallographic system, in the Cartesian coordinates for the computational experiment.

RELATIVISTIC ENERGY APPROACH AND MANY-BODY PERTURBATION THEORY TO COMPUTING ELECTRON-COLLISION CROSS-SECTIONS OF COMPLEX MULTIELECTRON IONS

An advanced relativistic energy approach combined with a relativistic many-body perturbation theory with ab initio zeroth approximation is used to calculate the electron-collision excitation cross-sections for complex multielectron systems. The relativistic many-body perturbation theory is used alongside the gauge-invariant scheme to generate an optimal Dirac-Kohn-Sham- Debye-Hückel one-electron representation. The results of relativistic calculation (taking into account the exchange and correlation corrections) of the electron collision cross-sections of excitation for the neon-like ion of the krypton are presented and compared with alternative results calculation on the basis of the R-matrix method in the Breit-Pauli approximation, in the relativistic distorted wave approximation and R- matrix method in combination with Dirac-Fock approximation

NUMERICAL STUDYING ENERGY PARAMETERS OF MULTIELECTRON ATOM IN A MAGNETIC FIELD: HELIUM

There are presented the results of calculating the energies of the helium atom energy in a homogeneous magnetic field on the basis of the new numerical quantum-mechanical approach. The approach is based on the numerical difference solution of the Schrödinger equation, the model potential method and the operator perturbation theory formalism. The obtained results on energy of the helium atom in dependence upon the magnetic field strength are compared with available theoretical results, obtained on the basis of alternative numerical Hartree-Fock and diagonalization methods.

THE STUDY OF HOMOGENEOUS AND HETEROGENEOUS SENSITIZED CRYSTALS OF CADMIUM SULFIDE. PART IV. FEATURES OF THE REVERSE PHOTOEXCITATION METHOD

For the first time, a reverse method of studying the spectral distribution curves of the photocurrent was applied, which allows to separate the contribution of equilibrium and non-equilibrium carriers. This publication is a continuation of the reviews [1-3]. In order to preserve the generality of the work, the numbering of sections is selected to be general. Numbers of formulas and figures are presented in sections. References to literature in each review are given individually. Cadmium sulfide crystals are used in our research as a convenient model material. The results obtained on them and the constructed models are also applied to other semiconductor substances.

RELATIVISTIC CALCULATION OF WAVELENGTHS AND E1 OSCILLATOR STRENGTHS IN Li-LIKE MULTICHARGED IONS AND GAUGE INVARIANCE PRINCIPLE

The spectral wavelengths and oscillator strengths for 1s22s (2S1/2) → 1s23p (2P1/2) transitions in the Li-like multicharged ions with the nuclear charge Z=28,30 are calculated on the basis of the combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth order optimized Dirac-Kohn-Sham one-particle approximation and gauge invariance principle performance. The comparison of the obtained results with available theoretical and experimental (compilated) data is performed. The important point is linked with an accurate accounting for the complex exchange-correlation (polarization) effect contributions and using the optimized one-quasiparticle representation in the relativistic many-body perturbation theory zeroth order that significantly provides a physically reasonable agreement between theory and precise experiment.

DYNAMICAL AND TOPOLOGICAL INVARIANTS OF NONLINEAR DYNAMICS OF THE CHAOTIC LASER DIODES WITH AN ADDITIONAL OPTICAL INJECTION

Nonlinear chaotic dynamics of the of the chaotic laser diodes with an additional optical injection is computed within rate equations model, based on the a set of rate equations for the slave laser electric complex amplitude and carrier density. To calculate the system dynamics in a chaotic regime the known chaos theory and non-linear analysis methods such as a correlation integral algorithm, the Lyapunov’s exponents and Kolmogorov entropy analysis are used. There are listed the data of computing dynamical and topological invariants such as the correlation, embedding and Kaplan-Yorke dimensions, Lyapunov’s exponents, Kolmogorov entropy etc. New data on topological and dynamical invariants are computed and firstly presented.

THEORETICAL STUDYING SPECTRAL CHARACTERISTICS OF Zn-LIKE IONS ON THE BASIS OF RELATIVISTIC MANY-BODY PERTURBATION THEORY

A theoretical study of the spectroscopic characteristics of Zn-like multiply charged ions is carried out within the framework of the relativistic many-body perturbation theory. The optimized Dirac-Kohn-Shem approximation was chosen as the zero approximation of the relativistic perturbation theory. Optimization has been fulfilled by means of introduction of the parameters to the Kohn-Sham exchange and correlation potentials and further minimization of the gauge-non-invariant contributions into radiation width of atomic levels with using relativistic orbital set, generated by the corresponding zeroth approximation Hamiltonian.