The new consistent approach to atom in a strong realistic laser field, based on the relativistic energy formalism (S-matrix adiabatic formalism), relativistic Dirac equation Green function method and relativistic many-body perturbation theory with the Dirac-Kohn-Sham zeroth approximation, is applied to studying the resonant multiphoton resonances shifts and widths and ionization cross-sections. An approach to treating the multiphoton atomic processes is outlined on example of H, Cs, Kr,Mg etc. Analysis shows that the shift and width of the multi-photon resonance line for the interaction "atom-multimode laser pulse" is greater than the corresponding shift and width for a case of the "atom-single-mode pulse" (the Lorenz pulse model) interaction. From the physical point of view it is naturally provided by action of the photon-correlation effects and influence of the laser pulse multi-modity.
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 order ab initio model potential optimized one-particle representation are used for precise computing the energy levels and radiative decay probabilities (radiation amplitudes) of heavy alkali elements, in particular, there are listed data for the 7s 1/2-np 1/2 , 3/2 , np 1/2 , 3/2-nd 3/2 , 5/2 (n=7-10) transitions in Fr and some E1 and E2 transitions in a single ionized Hg + atom. The comparison of the calculated values with available theoretical and experimental (compillated) data is performed..
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