|
|
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.
|
|
|
Quantum logic and projective spaces
Peksová, Lada ; Krýsl, Svatopluk (advisor) ; Cejnar, Pavel (referee)
A set of statements about the properties of a quantum system is looked at as at a partially ordered set of subspaces of finite or infinite dimensional Hilbert space. The operation of ordering is performed on a set of propositions comparing the truth values of these propositions and on the set of subspaces as the opera- tion of inclusion. Based on the required properties these structures are translated into operations on the lattice. The correspondence with Heisenberg uncertainty principle is shown there. Furthermore, it is shown that the lattices correspond- ing to the subspaces of infinite dimensional Hilbert space are not modular. This property is replaced with weaker property of orthomodularity, when operation of the negation is added. Following the work of G. Birkhoff and J. von Neumann, the structure of quantum logic is looked for in projective spaces, which are in- troduced either arithmetically or axiomatically. The examples of quantum logic, their physical implementation and eventual implementation in projective spaces are analysed. 1
|
|
|
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.
|
|
|
Photon strength functions in 196Pt from two-step gamma cascade measurement
Kloc, Michal ; Krtička, Milan (advisor) ; Cejnar, Pavel (referee)
Photon strength functions (PSFs), using the statistical approach to a nuclear decay, seem to be a suitable tool for the description of the electromagnetic transitions in a nucleus. Since the early 50's, when PSFs were first introduced, a plenty of theoretical models were proposed however their validity is still a question. In this work the data from the measurement of so called Two step cascades in the nucleus 196Pt using the reaction 195Pt(n,gamma)196Pt are processed. The experiment was performed at the Nuclear Physics Institute ASCR in Řež near Prague. We assume that these experimental spectra contain important information on PSFs. Comparison of the processed data with a few Monte Carlo simulations is also a part of this thesis.
|
|
|
Quantal and thermal phase transitions in atomic nuclei
Dvořák, Martin ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
In this bachelor work phase transitions in atomic nuclei are studied. The main attention is paid to quantal phase transitions between nuclear ground states of different symmetry. First, the interacting boson model in its simplest version, IBM-1, is introduced. The correspondence between the IBM and the geometric model of nuclei is indicated and possible shapes of the nucleus in the ground state are introduced. In the next step, critical and degenerated critical points of the potential derived from the IBM-1 are investigated in detail, especially their dependence on parameter values of the potential. Degenerated critical points are classified using the catastrophe theory. The special values of potential parameters are found for which phase transitions of the first and second order occur. Finally, the possibility of substitution of the potential by canonical catastrophic functions in a vicinity of degenerated critical points is discussed.
|
|
|
Jaderné kolektivní stupně volnosti a Skyrme funkcionál
Božík, Daniel ; Kvasil, Jan (advisor) ; Cejnar, Pavel (referee)
Title: Energy functional theories in nuclear physics Author: Daniel Božík Department: Institute of Particle and Nuclear Physics of Charles University Supervisor: prof. RNDr. Jan Kvasil, DrSc. Supervisor's e-mail address: kvasil@ipnp.troja.mff.cuni.cz Abstract: In the present work we study the giant resonances of the chain of even-even samarium nuclei 144−154 Sm. The numerical calculations are provided by a chain of numer- ical codes. Mean field is calculated by the HFB method for the Skyrme density functional and the residual interaction is included by the separable RPA method, which was devel- oped at IPNP MFF UK and JINR Dubna. The studied resonances are E1, E2 and M1. A special interest is paid to pygmy and scissor modes. The dependence of the pygmy modes on the deformation of nuclei is studied. The linear dependence of the integral scissor mode strength on the square of the nuclear deformation is verified within our microscopic model. Keywords: Skyrme functional, separable RPA, electric and magnetic giant resonances
|
|
|
Lorentz violation and supersymmetry
Vydrová, Zuzana ; Iorio, Alfredo (advisor) ; Cejnar, Pavel (referee)
This work studies Lorentz Violation in modications of Standard Model (minimal Standard Model Extension) using Noether theorem. For such theories there often is no way to fulll Euler-Lagrange expressions for all elds involved: the Noether theorem needs to be modied. In such case equivalence of symmetry and conservation vanishes.
|
|
|
Regular and chaotic collective motions of atomic nuclei
Hruška, Petr ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
This thesis deals with quantum chaos in the geometric collective model of atomic nuclei (GCM). The rst and second chapters introduce the derivation and analysis of basic aspects of the GCM. Two ways of quantization are introduced for zero rotations of the nucleus. The rst one takes into account only the vibrational degrees of freedom and does not correspond to real nuclei. The second way reects both vibrational and rotational degrees of freedom and leads to the standard GCM. The third chapter includes analytical calculations of matrix elements of the GCM in the harmonic oscillator basis. Some measures of chaos are described in the fourth chapter, including the method based on Peres lattices. Numerical results for both quantization methods are presented in the form of Peres lattices, which are compared with some adopted results of other measures of chaos.
|
|
| |
|
| |
guest ::
