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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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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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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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Quasispin models in quantum physics
Zymin, Andrii ; Stránský, Pavel (advisor) ; Kloc, Michal (referee)
Title: Quasispin models in quantum physics Author: Andrii Zymin Department: Institute of Particle and Nuclear Physics Supervisor: Mgr. Pavel Stránský, Ph.D., Institute of Particle and Nuclear Physics Abstract: The use of symmetries in quantum physics helps in a deeper understanding of physical systems and simplifies numerical calculations. This thesis studies models based on the SU(2) algebra, which, in spite of their apparent simplicity, show rather rich behavior and describe a wide spectrum of physical phenomena. We review various realizations of the SU(2) algebra (namely the spin, boson, and fermion realization) and present the most general quantum hamiltonian with one- and two-body interactions, constructed from the SU(2) generators. We perform the classical limit of the hamiltonian and show a numerical study of several particular examples. Keywords: dynamical symmetries, Lipkin model, su(2) algebra, quasispin
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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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Analysis of residual correlations in nuclear masses after application of Garvey-Kelson relations
Mičo, Samuel ; Stránský, Pavel (advisor) ; Knapp, František (referee)
This thesis is focused on the analysis of residual correlations bet- ween deviations of nuclear masses from Garvey-Kelson relations, which are local algebraic relations connecting masses of neighbouring nuclei. Properties of the correlation matrix determined by the deviations from Garvey-Kelson relations and by the calculated spectral correlations are consistent with the hypothesis formulated beforehand, that it is possible to understand the deviations as statis- tically independent fluctuations in a good agreement. Therefore, the masses of nuclei cannot be described by a global function of the number of protons and neutrons with an accuracy greater than the size of the deviations, i.e. with an accuracy better than an order of 100 keV. Principal component analysis shows that the largest residual correlations are located (i) in the area of magic numbers and (ii) between strongly deformed heavy nuclei.
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1/f noise in an algebraic model of molecular vibrations
Dušek, Jindřich ; Stránský, Pavel (advisor) ; Kadavý, Tomáš (referee)
1/f noise is commonly observed in many complex systems. In quantum systems it can serve as a chaos indicator without any reference to the properties of concrete RMT ensembles. We use the 1/f noise analysis to study a perturbed vibron model, which is a finite quantum system previously applied for description of linear molecules or a Bose-Einstein condensate. The results are in a partial agreement with the classical limit of our model with discrepancies observed for the integrable limit of the model. Such discrepancies are yet to be explained. We also suggest some improvements to our procedure, namely studying systems with a greater dimension, combining multiple systems with similar dimensions, or changing the length of the analysed time series. Lastly, we mention an inherent restriction of our procedure: the need for manual analysis of each system with particular parameters. This limitation restricts the usability of the 1/f noise analysis and it remains to be seen, whether it can be overcome. 1
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