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Quantum scarring in manybody systems
Škultéty, Richard ; Stránský, Pavel (advisor) ; Cejnar, Pavel (referee)
In this work, we will introduce the concept of quantum scarring. Quantum scarring refers to the states inside the chaotic parts of spectra, which significantly differ from predictions for chaotic states. In this work, we will focus on Quantum Many-Body Scars (QMBS), which deviate from the Eigenvector Thermalization Hypothesis (ETH) predictions. First, we will introduce the ETH and several ways in which the QMBS deviate from it; periodic revivals of non-eigenstate QMBS, anomalously low values of entanglement entropy, and localization of Husimi function in the classical limit. We will apply these methods to detect and study QMBS on coupled Lipkin models. 1
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The role of non-Gaussian entanglement of continuous variable quantum states in quatum technologies
Matulík, Michal ; Marek, Petr (advisor) ; Cejnar, Pavel (referee)
We present an effort to find a measure of non-Gaussianity of non-Gaussian states. We compute the difference between the logarithmic negativities of a non-Gaussian state and its Gaussified form as a non-Gaussian entanglement resource. We use the latter to assess the resource content of non-Gaussianity of experimentally relevant state - two- mode squeezed vacuum with a subtracted photon. We also used symplectic analysis to discard the Gaussian entanglement. Therefore the measure is reduced to the logarithmic negativity of a non-Gaussian state only. We compare the measure with the Wigner distribution and its negativity and discuss the results. 1
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Measures of quantum entanglement
Bajo, Igor ; Cejnar, Pavel (advisor) ; Stránský, Pavel (referee)
We present measures of bipartite entanglement in the multiparticle spin-1/2 systems. We also touch on the phenomenon of Quantum Phase Transitions and spin coupling. In the end we create a Python code for graphical visualisation of entanglement in relation to ground state energy behaviour. 1
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Periodically driven quantum systems
Honsa, Lukáš ; Cejnar, Pavel (advisor) ; Šindelka, Milan (referee)
We present theoretical methods for studying quantum mechanical systems subjected to fast periodic driving and apply them to model systems with long-range interaction. We provide a comparison between the methods and insight facilitated by these methods. The methods recently occurred in scientific papers, which supports the need for a scrutinized exposition of the theory. One of the main objects of the theory is a so-called Floquet Hamiltonian-an artificial stationary Hamiltonian describing important features of a quantum system. The methods construct Floquet Hamiltonians in the form of series in the powers of the time period. We present the spectra of Floquet Hamiltonians-the so-called quasienergy spectra-computed by the methods and computed numerically (with higher precision). The quasienergy spectra were computed using various approximations of Floquet Hamiltonians and compared. We discuss an interesting topic of the classical limit of an artificial stationary system. We also mention the kicked rotor system and its connection with the kicked top system-one of our model systems. In summary, the method characterized by simultaneous construction of a Floquet Hamiltonian and a so-called kick operator (operator capturing fast changes of the system) was found universal and accurate. The thesis presents an...
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Quantum chaos in finite many-body systems
Novotný, Jakub ; Stránský, Pavel (advisor) ; Cejnar, Pavel (referee)
In this work, we show, that relative oscillations in asymptotic times of microcanonical Out-of-Time-Order correlators (OTOCs) are suppressed by chaos with the size of the sys- tem. Therefore they can serve as an indicator of quantum chaos in quantum systems. We demonstrate this phenomenon on numerical results of the Out-of-Time-Order correlators from a model with hamiltonian based on the u(3) algebra. Firstly we prove, that this model can be used not only for the description of molecular vibrations, but also Bose- Einstein condensate. Then we employ several methods for the analysis of both quantum and classical chaos, namely spectral statistics such as Nearest Neighbour Spacing Distri- bution and Brody distribution, Inverse Participation Ratio, Poincaré sections, Lyapunov exponent, and the chaotic fraction of classical phase space. We compare these results with relative oscillations of microcanonical Out-of-Time-Order correlators and show, that their suppression corresponds with the chaoticity of the quantum system and the fraction of chaotic regions of the classical phase space. 1
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Geometric approach to externally driven quantum systems
Střeleček, Jan ; Cejnar, Pavel (advisor) ; Novotný, Jiří (referee)
The theory of quantum driving of parametric driven Hamiltonians is presented and reformulated using the language of differential geometry. The general fidelity driving in a two-level Hamiltonian system is then analyzed with the particular importance of fidelity time dependence. For the Lipkin-Meshkov-Glick model, the geometrical structure of its energy state manifolds is calculated with an aim to analyze adiabatic and close adiabatic drivings. 1
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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
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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)
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A model of resonant collisions of electrons with molecules and molecular ions
Váňa, Martin ; Houfek, Karel (advisor) ; Cejnar, Pavel (referee) ; Mašín, Zdeněk (referee)
A two-dimensional model of the resonant electron-molecule 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 time-dependent framework and solved numerically using the finite-element method with the discrete variable representation basis, the exterior complex scaling method and the generalized Crank-Nicolson method. On the model of electron-molecule collisions we illustrate how the time-dependent 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...
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