Abstract. Work is devoted to the development of the theoretical foundations of the universal complex chaos-geometric and quantum-dynamic approach that consistently includes a number of new quantum models and a number of new or improved methods of analysis (correlation integral, fractal analysis, algorithms, average mutual information, false nearest neighbors, Lyapunov exponents, surrogate data, non-linear prediction, spectral methods, etc.) to solve problems quantitatively complete modeling and analysis of chaotic dynamics of nonlinear processes in atomic and molecular systems in a uniform and alternating electromagnetic field and quantum generator, laser systems and devices (including fibers, semiconductor lasers with feedback et al.). For considered class of systems and devices there are theoretically studied scenarios of generating chaos, obtained complete quantitative data on the chaos characteristics and different modes of operation.

The paper is devoted to problem of development of new mathematical and computational tools for analysis and processing the measurements data of chaotic quantum and laser systems and quantum devices (sensors). The chaos-geometric approach proposed includes a combined group of non-linear analysis and chaos theory methods such as the autocorrelation function method, multi-fractal formalism, wavelet analysis, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, Lyapunov's exponents and Kolmogorov entropy analysis, surrogate data method, memory functions, neural networks algorithms. There are presented the most effective schemes for computing the Lyapunov's exponents spectrum, Kaplan-Yorke dimension, Kolmogorov entropy etc.

The combined relativistic energy approach and relativistic many-body perturbation theory with the zeroth Dirac-Fock-Sham approximation are used for computing the thermal Blackbody radiation ionization characteristics of the alkali Rydberg atoms, in particular, the sodium in Rydberg states with principal quantum number n=10-100. The detailed analysis of the data of computing ionization rates for the Rydberg sodium atom demonstrates physically reasonable agreement between the theoretical and experimental data. The accuracy of the theoretical data is provided by a correctness of the corresponding relativistic wave functions and accounting for the exchange-correlation effects.

It is developed the optimized version of relativistic operator perturbation theory approach to calculation of the Stark resonances energies characteristics (energies and widths) for the multielectron atomic systems in an electromagnetic field. A new approach allows to perform an accurate, consistent treatment of a strong field DC(AC) Stark effect and includes the physically reasonable distorted-waves approximation in the frame of the formally exact relativistic quantummechanical procedure. As illustration, some test data for the Stark resonances energies and widths Sensor Electronics and Мicrosystem Technologies 2018-T. 15, № 4 51 in the heavy multielectron atoms (caesium, francium) are presented and compared with results of calculations within the alternative consistent sophisticated methods etc.

It has been carried out sensing and calculating probabilities and oscillator strengths of a number of radiative transitions in the spectra of heavy Rydberg atoms of alkaline elements on the basis of new relativistic model potential method in the framework of gauge-invariant perturbation theory and relativistic energy approach.. It has been shown that that a new approach provides a precise accounting exchange-correlation effects, including effect of essentially non-Coulomb grouping of Rydberg levels, pressure continuum. There are received precise data on energy and spectroscopic parameters energy, radiation width, amplitude transitions, the lifetime) for Rydberg atoms Rb, Cs, Fr, particularly, transitions nS½→n'P½, 3 / 2 (n=5,6; n'=10-70), nP½,3.2→n'D 3 / 2 , 5 / 2 (n=5,6; n'=10-80) in the Rb, Cs spectra; for Rydberg Fr there are in most first calculated and predicted spectroscopic data on transition amplitude, lifetime of Rydberg states and transitions 7S½-nP½, 3 / 2 , 7P½,3.2-nD 3 / 2 , 5 / 2 (n=20-80). Data obtained can be used in carrying out new types of radiative quantum sensors and frequency standards.