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Comparison of frequency stability of laser wavelength standards over photonic networks
Pravdová, Lenka ; Hrabina, Jan ; Čížek, Martin ; Lazar, Josef ; Číp, Ondřej
In our work we present a metrological ampaign in which the stability of the 1540 nm normal laser located at the CESNET workplace in Prague was compared with the wavelength of the supercoherent laser transmitted from the ÚPT workplace in Brno via the 306 km phase-coherent transfer line Brno - Prague. The assembled acetylene standard was transferred to the CESNET workplace and a unit receiving coherent wave from the supercoherent laser stabilized by the optical frequency comb and the H-maser at the ISI workplace in Brno was put into operation. The optical frequency mixer with a photodetector recorded a frequency response between the acetylene optical frequency normal and the supercoherent laser distributed over the photonic network whose stability is given by the H-maser in the 15th order. We have verified that the laser normal meets the requirements of the BIMP Recommendation for the Practical Implementation of the Meter Standard.
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Utilization of hydrogen cyanide as an absorption media for laser spectroscopy
Hošek, Martin ; Řeřucha, Šimon ; Pravdová, Lenka ; Čížek, Martin ; Hrabina, Jan ; Číp, Ondřej
The main goal of our investigation is the use of hydrogen cyanide (concretely isotope H13C14N) as absorption medium for realisation of etalon of optical frequency. The advantage of HCN over typically used acetylene (isotopes 13C2H2 and 12C2H2) is the better availability and also the wider absorption spectrum in the 1550 nm wavelength band (telecommunication band). The hyperfine transitions in HCN were investigated in the 90‘, but because of technological limitations the measured data are not as precise as the data for C2H2. We aim on use of more developed methods (saturated absorption spectroscopy, optical frequency lock, beat-note against the optical frequency comb) for the measurement of more precise data of absorption lines of HCN. Our other goals will be to obtain the data enough precise to allow the use of them in Mise en pratique.
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Stable optical frequency transfer between ISI and CESNET workplaces
Čížek, Martin ; Pravdová, Lenka ; Hucl, Václav ; Jelínek, Michal ; Hrabina, Jan ; Řeřucha, Šimon ; Mikel, Břetislav ; Lazar, Josef ; Číp, Ondřej ; Smotlacha, V. ; Havliš, O. ; Vojtěch, J.
The contribution reports on the current state of a 306km long experimental line for transfering stable optical frequency from a telecommunication band laser standard between ISI CAS (Brno) and CESNET (Prague). The bidirectional link uses a telecommunication fiber with a dedicated DWDM window of 1540-1546 nm.1540-1546 nm. In the Czech rep. this technology can be utilized currently in two fields: remote comparisons of optical frequency standards and remote callibration of instruments (optical spectral analyzers) in industrial applications that do not allow transporting the device to a specialized laboratory. The stability of the optical frequency transfer was evaluated. A long-term measurement of transport delay was conducted. \n
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Singular Behavior of the Hartree-Fock Equations
Uhlířová, Tereza ; Zamastil, Jaroslav (advisor) ; Čížek, Martin (referee)
The non-linear Hartree-Fock (HF) equations are usually solved via the iterative self-consistent field method. However, there is no a priori guarantee of convergence, especially in systems with strong electron correlation where symmetry breaking occurs. This work focuses on closed- shell systems in the HF approximation and the (in)stability of the found solutions, and proposes new deterministic methods for the localization of both symmetry-adapted and broken symmetry solutions. We employ a perturbative method and show how one can always obtain a symmetry-adapted solution of the HF equations. We also determine the radius of convergence, related to the existence of at least one bound state, of the perturbative series. Next, we rederive the matrix of stability and adapt it to spin and orbital symmetry. Calculation of higher energy variations follows, first in terms of spin-orbitals and then orbitals. Motivated by the investigation of the structure of a broken-symmetry solution, we propose a new deterministic method for the localization of a broken-symmetry solution. The general expressions are verified by reformulating the stability conditions for simple cases. The proposed methods are successfully applied to helium-, beryllium- and neon-like systems.
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Collisions of electrons with diatomic molecules
Matoušek, Mikuláš ; Houfek, Karel (advisor) ; Čížek, Martin (referee)
For succesfully carrying out R-matrix calculations, a good description of the excited states of the neutral molecule around the equilibrium is needed, obtained by an ab-initio method in a relatively small basis. It is also neccesary to have potential curves of the neutral molecule and the anion that are consistent with the experimentally obtained values for the molecule and are used to set up the initial parameters of these calculations. In this work we are trying to find a description of the excited states and to obtain reference curves in order to perform R-matrix calculations for two molecules, BeH and OH. For BeH we propose a description of the excited states by the SA-CASSCF method with an active space of 6,2,2,0 and in the aug-cc-pVDZ basis. Similarly for OH a description by the SA-CASSCF method with an active space of 6,2,2,0 or 7,3,3,0 and an in an aug-cc-pVDZ basis should be used, where we have also found a setting of the weights of the states in the SA-CAS-SCF method significantly improving the shape of the curves. We have not yet been able to perform the R-matrix calculations because of insufficient time. 1
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Quantization of dynamics of molecular rattleback.
Bačo, Zsolt ; Čížek, Martin (advisor) ; Čurík, Roman (referee)
Title: Quantization of dynamics of molecular rattleback Author: Zsolt Bačo Institute: Institute of Theoretical Physics Supervisor: doc. RNDr. Martin Čížek, Ph.D., Institute of Theoretical Physics Abstract: This thesis has a theoretical character and is dealing with the prob- lem of a molecular rattleback from the quantum perspective, based on knowledge from classical physics of the same system. It is a rotor which doesn't conserve a direction of rotation. The aim is a quantization of the system's energy, what is an objective for a matrix representation of hamiltonian and consecutive diago- nalization, for what a suitable mathematical apparatus is needed to be built. In this thesis, there are derivated equations in detail, which are needed for matrix elements of hamiltonian. The next aim is a study of spectrum of hamiltonian gained by numerical computes, specifically a convergence of approximate values and their statistics. Based on the spectrum's statistics, there is a discussion about the chaotic character of the system. The main contribution of this thesis is the method of computing energetic levels of rotating objects in potential. Keywords: quantum dynamics, energy spectrum, rotational movement, rattleback
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The procedures for the reduction of tax evasion in the field of value added tax
ČÍŽEK, Martin
This dissertation is dedicated to tax fraud in the area of VAT (Value Added Tax). First of all, VAT terms are primarily defined according to current VAT law and also with respect to the harmonization of this tax in the European Union. The next section focuses on the VAT authority and individual constituents which contribute to the tax authority, as well as compliance with its requirements. The main part of the dissertation is dedicated to the forms of tax evasion most frequently practiced in the Czech Republic. The most widespread tax fraud, carousel fraud, is explained and described with the help of diagrams in a separate section. This matter is followed by the issue of the ways in which tax fraud is being prevented, the means of which are examined individually. The process of VAT collections in the federal budget is analyzed, as is the growth of VAT in connection with that of the GNP, in the second half of the dissertation. Subsequently, there is an analysis of the growth of VAT due to higher tax rates, and as a result of the introduction of more efficient tax collection procedures for added value and the implementation of different measures against tax fraud. The analyses are followed by potential procedures and remarks which could lead to a further reduction of criminal activity in this tax area.
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Classical and quantum chaotic dynamics in reactive scattering of atoms and molecules.
Trnka, Jiří ; Čížek, Martin (advisor) ; Houfek, Karel (referee)
The thesis deals with quantum reaction dynamics of three-particle systems. The thesis summarizes main theoretical results about three-body problem in quantum mechanics. A simple two dimensional model of three-particle system corresponding to atom-diatom collision was studied as a part of this thesis. The model allows for vibrational excitation and reaction processes. Solution based on distorted-wave method and Schwinger variational principle is proposed to solve the model. Proposed method of solution is then applied to a system of three coupled Morse potential energy surfaces. Probabilities of possible proces- ses depending on energy of incoming particle were calculated using the proposed method of solution for two variants of coupled Morse PESs. 1
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Foreign Legions Waffen-SS
Kacerovský, Tomáš ; Čížek, Martin (advisor) ; Šmidrkal, Václav (referee)
This bachelor thesis focuses on the foreign Waffen-SS legions that had been fighting alongside the German army in the Second World War. The Nazis came out with the idea of establishing an international military force, that would consist of citizens of the currently occupied countries. The key thesis is based on the thought that the Nazis managed to create such legions, that consisted of men who decided to fight against the Soviet Union and Bolshevism, led by the idea of being a part of a so called European army. The first chapter focuses on the elementary factors within the establishment of the foreign legions. Though the Nazis knew they had been acting against their own ideology, and Adolf Hitler himself views the legions rather sceptically, Waffen-SS needed more soldiers in favour of becoming a fully competent armed force. The second chapter speaks about the ordinary volunteers, who decided to serve in the legions and about their motivation. This chapter is also facing an issue in terms of distinguishing each sort of the legion members, who served based on various different reasons and ideas. The third chapter refers about the important and famous people who served in the foreign legions or who had been publicly supporting them and had been calling other potential volunteers to arms. The last...
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