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Adiabatic quantum computation
Charamza, Lukáš ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
In this thesis we summarize the principles of quantum computing. We specifically consider adiabatic quantum computing, whose principles are explained and shown on several examples. To explain the principle of adiabatic quantum computing we review the adiabatic theorem. We also outline possibility of using a particular Hamiltonian by Berry, which enables us to evolve system adiabatically in arbitrarily short time. In the final part of this thesis, we explain the concept of quantum phase transitions. We discuss a relationship between quantum phase transitions and adiabatic quantum computing and show that adiabatic quantum computing scales polynomially with the number of qubits only for quantum phase transitions of second or higher order. Powered by TCPDF (www.tcpdf.org)
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Kvantové kritické jevy v konečných systémech
Kloc, Michal ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
Singularities in quantum spectra - ground state and excited-state quantum phase transitions - are often connected with singularities in the classical limit of the system and have influence on other properties, such as quantum entanglement, as well. In the first part of the thesis we study quantum phase transitions within the U(2)-based Lipkin model. The relation between quasistationary points of the classical potential and the respective singularities in the spectrum is shown. In the second part, a system of two-level atoms interacting with electromagnetic field in an optical cavity is studied within two simplified models (non-integrable Dicke model and its integrable approximation known as Jaynes-Cummings model). The behaviour of quantum entanglement in these models is shown with a focus on the vicinity of the singular points.
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Processing of two-step γ cascade data from 151Eu(n,γ)152Eu reaction
Schusser, Jakub ; Krtička, Milan (advisor) ; Cejnar, Pavel (referee)
1 Photon strength functions in terms of statistical approach to a nuclear decay describe the probability distribution of photon emission by given nucleus. They can be studied using two step gamma cascades. The two step gamma cascade method was firstly introduced in fifties of the 20th century. Our aim is to study two step gamma cascades following thermal neutron capture in 151 Eu. The experiment was performed at the Nuclear Physics Institute ASCR in Řež near Prague. The acquired emission spectra of photons from thermal neutron capture will be processed by energetic and efficiency calibration and after further processing will be compared to the output of theoretical models.
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Precursors of phase transitions in quantum systems
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
In this diploma thesis precursors of quantum phase transitions in finite many-body systems are studied. The main attention is paid to the mechanism, how nonanalytic behaviour of the ground state is generated for certain critical values of real control parameters. It is shown that nonanalytic behaviour of energy levels and eigenstates is closely connected with exceptional points of the hamiltonian, which are points in control parameter space extended into a complex domain where at least two eigenvalues and corresponding eigenvectors coincide. Differences in the distribution of exceptional points in the complex plane of control parameter for the first and second order phase transitions and also evolutions of the position of exceptional points with increasing particle number are discussed.
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Dynamical symmetries in physics
Hájek, Pavel ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
The aim of this thesis is to provide a definition of dynamical symme- try and to study its properties within simple quantum systems. In particular, I investigate Kepler's problem and the isotropic harmonic oscillator. Dynamical sy- mmetry is a kind of higher symmetry which is broken in a specific way. Definition of dynamical group and quantum mechanical system is presented. Subsequently, a definition of quantum degrees of freedom and quantum integrability is propo- sed. I mention briefly a possibility of finding the generators of dynamical group by considering time dependent constants of motion.
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Photon strength functuins in 160Tb from two-step gamma cascade measurement
Kroll, Jiří ; Krtička, Milan (advisor) ; Cejnar, Pavel (referee)
Title: Photon strength functions in nucleus 160 Tb from the two-step γ cascades measurements Author: Jiří Kroll Department: Institute of Particle and Nuclear Physics Supervisor: Mgr. Milan Krtička, Ph.D. Supervisor's e-mail address: krticka@ipnp.troja.mff.cuni.cz Abstract: Photon strength functions have been a subject of a study for more than fifty years. A number of models was proposed to describe experimental data during that time. However, the correctness of these models is still very questionable and its verification is the subject of very intensive experimental and theoretical activity at the present time. In the present work the analysis of measurements of the two-step γ cascades following the slow neutron capture on the 159 Tb nucleus is used for study of photon strength functions. Results of the experimental data analysis are compared with the outputs of the Monte Carlo simulations based on the validity of so called Extreme Statistical Model. Comparison of experimental data with outcomes of simulations thus becomes the basic tool for studying correctness of theoretical models. Keywords: Photon strength function, Energy level density, Extreme Statistical Model
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Quantum entanglement
Matulík, Michal ; Cejnar, Pavel (advisor) ; Stránský, Pavel (referee)
We present overview of discussion among the greatest physicists from first half of last century. The discussion led to discovery of quantum entanglement. We build mathemat- ical formalism of quantum entanglement for bipartite systems. With that formalism we count quantum entanglement in system given by Lipkin Hamiltonian. We plot the results in graphs and we dicuss the results. 1
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Bridge - computing optimal strategies
Cejnar, Pavel
We give a theoretical model of the game Bridge and its simplified variation. We construct an algorithm for the best response against any given strategy in this model. Then we construct an algorithm for an optimal strategy of the players based on the Brown-Robinson iterative method and we extend this method. In the appendix we also describe algorithms based on heuristic principles that are used in commercial programs.
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Dynamical signatures of quantum phase transitions for excited states
Dolejší, Jakub ; Cejnar, Pavel (advisor) ; Kloc, Michal (referee)
Dynamical signatures of quantum phase transitions for excited states Jakub Dolejší Abstract We study the impact of quantum phase transitions (QPTs) and excited- state quantum phase transitions (ESQPTs) on the validity of the adiabatic approximation for a slowly varying Hamiltonian. We compare two cases, when the initial state is the ground state of the initial Hamiltonian and when the initial state is a statistical mixture of excited states induced by a finite temperature. We use the Lipkin-Meshkov-Glick model of a spin lattice and obtain an abruptly decreasing scaling law of the ground-state population with a growing system size N. We comment on the justifiability of using the Landau-Zener formula to make a quantitative prediction in the case of a first-order and a second-order QPT. To achieve a truly adiabatic evolution in the thermodynamic limit, one would need to perform the Hamiltonian change during an impossibly long time period. It is possible, however, to obtain the same adiabatic final state in a given finite time period by inducing the quantum evolution with another Hamiltonian specifically devised for this purpose, thus employing the so called adiabatic shortcut. We verify the validity of adiabatic shortcuts in the presence of QPTs and ESQPTs and study the costs of performing such adiabatic...
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Quantum phase transitions in systems with a finite number of degrees of freedom
Kloc, Michal ; Cejnar, Pavel (advisor) ; Schaller, Gernot (referee) ; Šindelka, Milan (referee)
In the thesis we investigate and classify critical phenomena in the extended Dicke model (EDM) which describes the interaction between two-level atoms and a single-mode bosonic field (schematic model for cavity quantum electrodynamics). The model belongs to the class of so-called finite models, which keep the number of degrees of freedom f constant independently on the size of the system N . The important property of these systems is that the thermodynamic limit N → ∞ coincides with the classical limit ħ → 0. This allows us to study various quantum critical phenomena, in particular the ground-state quantum phase transitions (QPTs) and the excited-state quantum phase transitions (ESQPTs), by means of semiclassical methods. Using the semiclassical approach we identify and classify the QPTs and ESQPTs in various settings of the EDM and make a link to thermal phase transitions. We study the entanglement properties of both the ground state and the excited states as a function of the atom-field interaction strength. In the integrable version of the EDM we make a link between the ESQPT and monodromy, and discuss its effect on classical dynamics. The fate of monodromy under a non-integrable perturbation is observed. The dynamical consequences of the ESQPTs are examined using quantum quenches. The influence of the...
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