
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 twolevel atoms and a singlemode bosonic field (schematic model for cavity quantum electrodynamics). The model belongs to the class of socalled 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 groundstate quantum phase transitions (QPTs) and the excitedstate 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 atomfield 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 nonintegrable perturbation is observed. The dynamical consequences of the ESQPTs are examined using quantum quenches. The influence of the...


Relation between Schrödinger equation and diffusion equation
Poprocký, Mojmír ; Stránský, Pavel (advisor) ; Cejnar, Pavel (referee)
The Schrodinger's equation and the diffusion equation can be written in a similar form. While the Schrodinger's equation is complex, the diffusion equation is real. In this thesis we wish to outline similarities of both equations. We present a way to treat a problem in nonrelativistic quantum mechanics as a diffusion process. This shows that under certain circumstances both theories are equivalent. We demonstrate this on a few simple examples.


Subtle Effects in Atmos and Molecules
Šimsa, Daniel ; Zamastil, Jaroslav (advisor) ; Cejnar, Pavel (referee) ; Šindelka, Milan (referee)
The thesis is divided into two parts. The first part deals with radiative cor rections in muonic hydrogen. The effect of vacuum polarization is studied, and the simplified derivation of the WichmannKroll potential is presented. The en ergy shift caused by vacuum polarization to the Lamb shift in muonic hydrogen is calculated and it agrees with results in literature. Further, the concept of the extended Bethe logarithm is introduced and its advantages are shown and used to calculate the combined selfenergy vacuum polarization contribution to the Lamb shift in muonic hydrogen. The results given here are more accurate and somewhat different from others given in literature. In the second part, the groundstate en ergy splitting due to the tunneling in a twodimensional doublewell potential is calculated. A systematic WKB expansion of the energy splitting is given. An in terplay between curvature of the classical tunneling path and quantum nature of motion is observed. A series is found that describes systems with strong coupling like the proton transfer in malonaldehyde. The results show a strong sensitivity of the splitting on slight variations of the parameters entering the Hamiltonian linearly. This indicates a presence of quantum chaos in this problem. 1


Dynamics of externally driven quantum systems
Dolejší, Jakub ; Cejnar, Pavel (advisor) ; Stránský, Pavel (referee)
Dynamics of externally driven quantum systems Jakub Dolejší Abstract We present the concept of an excitedstate quantum phase transition and analyse its influence on the nonequilibrium dynamics after a quantum quench in the Lipkin model. We show that if the energy distribution of the initial state after the quench is centred at the critical energy, the survival probability of the initial state evolves in an anomalous way. Keywords Quantum phase transitions, Excitedstate quantum phase transitions, Quantum quenches, Lipkin model 1


A model of resonant collisions of electrons with molecules and molecular ions
Váňa, Martin ; Houfek, Karel (advisor) ; Cejnar, Pavel (referee) ; Mašín, Zdeněk (referee)
A twodimensional model of the resonant electronmolecule collision processes with one nuclear and one electronic degree of freedom introduced by Houfek, Rescigno and McCurdy [Phys. Rev. A 73, 032721 (2006)] and a similar two dimensional model of the dissociative recombination with potential proposed by Hamilton [Ph.D. thesis, University of Colorado, (2003)] are formulated within the timedependent framework and solved numerically using the finiteelement method with the discrete variable representation basis, the exterior complex scaling method and the generalized CrankNicolson method. On the model of electronmolecule collisions we illustrate how the timedependent calculations can provide a deep insight into the origin of oscillatory structures in the vibrational excitation cross sections if one evaluates the cross sections not only at sufficiently large time to obtain the final cross sections, but rather at several characteristic times which are given by the evolution of the system. With use of the time dependent calculations we demonstrate the complex nature of the dissociative recombination model dynamics and we propose the interpretation of the recom bination process mechanism. We also propose few techniques for the explanation of the sharp structures in the dissociative recombination cross sections...


Studium fotonových silových funkcí z termálního záchytu neutronů
Bauer, Karel ; Krtička, Milan (advisor) ; Cejnar, Pavel (referee)
A subject of this thesis is to gain information on absolute photon strength function below the neutron separation energy. This energy range is known as a "lowtail" energy region of E1 resonance. The absolute photon strength function is obtained by normalizing the total average intensity for several energy ranges to the average intensities from thermal neutron capture spectrum for which an absolute calibration is experimentally known. The absolute photon strength function is investigated by means of statistical method. Everything seems to be compatible with information on studied Gd isotopes. However, disclosed method can potentially lead to rejection of combination of PSF and LD models. Powered by TCPDF (www.tcpdf.org)


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 manybody 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.


Studium fotonových silových funkcí z termálního záchytu neutronů
Bauer, Karel ; Krtička, Milan (advisor) ; Cejnar, Pavel (referee)
This thesis deals with the description of $\gamma$ray deexcitation of neutron resonances produced in thermal neutron capture below neutron separation energy. A subject of this thesis is obtaining information on absolute value of \textit{photon strength function} (PSF) achieved from primary transitions in thermal neutron capture. The aim is to map and bring new information on absolute value of photon strength function (PSF) in $^{156}$Gd and $^{158}$Gd. The method which was used in this thesis can lead to refusion of several models of PSF a level density. Powered by TCPDF (www.tcpdf.org)


Quantum computing in manybody physics
Brandejs, Jan ; Cejnar, Pavel (advisor) ; Knapp, František (referee)
Název práce: Kvantové výpočty v mnohočásticové fyzice Autor: Jan Brandejs Katedra: Ústav částicové a jaderné fyziky Vedoucí bakalářské práce: prof. RNDr. Pavel Cejnar, Dr., DSc., Ústav částicové a jaderné fyziky Abstrakt: Při simulaci mnohočásticových kvantových systém· obvykle dochází k exponenciální explozi výpočetní složitosti. Kvantové počítače umožňují ten to problém principiálně vyřešit. Díky práci R. Feynmanna je známo, že axiomy teorie složitosti vychází z fyzikálních zákon·. Situace se změní, zavedemeli do výpočetního procesu mimo klasické fyziky i kvantovou teorii. Ukazuje se, že pro efektivní simulaci kvantového systému je vhodné použít jiný, lépe kontrolovatelný kvantový systém. Realizace výpočtu s využitím qbit· a kvantového paralelismu pak ve vybraných případech vede k zásadní redukci složitosti. Kvantové počítače potenciálně umožňují realizaci výpočt· a simulací, které jsou s klasickými počíta či prakticky neproveditelné. Zejména na poli kvantové chemie vyvstává možnost přímočaré aplikace. Tato práce je zaměřena na použití kvantových počítač· pro mnohočásticové problémy a obsahuje analýzu složitosti kvantové simulace atomo vých jader. Klíčová slova: kvantový počítač, kvantová simulace, mnohočásticová fyzika


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)
