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Level spacing distribution of quantum systems
Škultéty, Richard ; Augustovičová, Lucie (advisor) ; Picková, Irena (referee)
The aim of this work is to get acquainted with the topic of quantum chaos and statistical methods used to quantify it. In the first part of this work I will show the definition of both classical and quantum chaos. I will introduce NNS method, which studies quantum chaos as correlations between levels in the spectrum. In the second part of my work I will describe basic methods used to work with data in a form of probability density. In the third part this work I will focus on methods that are specific for quantum chaos. To simulate a quantum chaotic system I will use the basics of random matrix theory. I will introduce unfolding and I will study the distribution of NNS for simulated spectra. To quantify quantum chaos I will use Brody distribution. In the last part of this work I will apply above mentioned methods on spectra of real particles.
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Quantum dynamics of small molecules
Augustovičová, Lucie ; Soldán, Pavel (advisor) ; Čurík, Roman (referee) ; Fišer, Jiří (referee)
This thesis deals with the process of molecular ions formation in interstellar space, which played an important role in the early Universe. A large part of the work focuses on the theoretical study of quantum dynamics of the process of radiative association pre- dominantly induced by dipole transitions. The effect of quadrupole transitions on the radiative association have also been taken into account, which has been studied for the first time. Furthermore, spectroscopic characteristics of rovibronic transitions of selected di- atomic ions for the study of cosmological variability of fundamental constants were determined. The main outcomes of the thesis include the characterization of depopulation of metastable levels He (23S) and He (21S) due to radiative collisions with hydrogen, helium and lithium ions, i. e. He + A+ → HeA+ + hν. Within the study quantum dynamics calculations were carried out using a fully quan- tal approach. Studied spontaneous and stimulated processes on a specific spin manifold were characterized by energy-dependent cross sections and temperature-dependent rate coefficients. Compared to previous published works by other authors highly excited electronic states are considered. The results showed that a) the spontaneous radiative association contributes significantly to the...
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Level spacing distribution of quantum systems
Škultéty, Richard ; Augustovičová, Lucie (advisor) ; Picková, Irena (referee)
The aim of this work is to get acquainted with the topic of quantum chaos and statistical methods used to quantify it. In the first part of this work I will show the definition of both classical and quantum chaos. I will introduce NNS method, which studies quantum chaos as correlations between levels in the spectrum. In the second part of my work I will describe basic methods used to work with data in a form of probability density. In the third part this work I will focus on methods that are specific for quantum chaos. To simulate a quantum chaotic system I will use the basics of random matrix theory. I will introduce unfolding and I will study the distribution of NNS for simulated spectra. To quantify quantum chaos I will use Brody distribution. In the last part of this work I will apply above mentioned methods on spectra of real particles.
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Zeeman effect in 2Pi molecules
Menšíková, Jana ; Augustovičová, Lucie (advisor) ; Tichý, Vladimír (referee)
This research work deals with the fine structure of spectral lines in molecules. These are represented by OH molecule which plays an important role in spectroscopy. While investigating molecular spectra, one must take into account the electronic orbital angular momentum, the spin angular momentum and the rotational angular momentum. We are going to form the effective Hamiltonian of the fine-structure interactions, afterwards we are going to programme the Zeeman Hamiltonian which is dominated by contributions of the electronic orbital and spin isotropic Zeeman effects, and we analyse the influence of parity on lines splitting in external magnetic field. Investigating of Zeeman effect is a significant method of determining the intensity of magnetic fields in molecular clouds or sunspots.
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Quantum dynamics of small molecules
Augustovičová, Lucie ; Soldán, Pavel (advisor) ; Čurík, Roman (referee) ; Fišer, Jiří (referee)
This thesis deals with the process of molecular ions formation in interstellar space, which played an important role in the early Universe. A large part of the work focuses on the theoretical study of quantum dynamics of the process of radiative association pre- dominantly induced by dipole transitions. The effect of quadrupole transitions on the radiative association have also been taken into account, which has been studied for the first time. Furthermore, spectroscopic characteristics of rovibronic transitions of selected di- atomic ions for the study of cosmological variability of fundamental constants were determined. The main outcomes of the thesis include the characterization of depopulation of metastable levels He (23S) and He (21S) due to radiative collisions with hydrogen, helium and lithium ions, i. e. He + A+ → HeA+ + hν. Within the study quantum dynamics calculations were carried out using a fully quan- tal approach. Studied spontaneous and stimulated processes on a specific spin manifold were characterized by energy-dependent cross sections and temperature-dependent rate coefficients. Compared to previous published works by other authors highly excited electronic states are considered. The results showed that a) the spontaneous radiative association contributes significantly to the...
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