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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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Level spacing distribution of quantum systems
Škultéty, Richard ; Augustovičová, Lucie (advisor) ; Picková, Irena (referee)
The aim of this work is to get acquainted with the topic of quantum chaos and statistical methods used to quantify it. In the first part of this work I will show the definition of both classical and quantum chaos. I will introduce NNS method, which studies quantum chaos as correlations between levels in the spectrum. In the second part of my work I will describe basic methods used to work with data in a form of probability density. In the third part this work I will focus on methods that are specific for quantum chaos. To simulate a quantum chaotic system I will use the basics of random matrix theory. I will introduce unfolding and I will study the distribution of NNS for simulated spectra. To quantify quantum chaos I will use Brody distribution. In the last part of this work I will apply above mentioned methods on spectra of real particles.
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Level spacing distribution of quantum systems
Škultéty, Richard ; Augustovičová, Lucie (advisor) ; Picková, Irena (referee)
The aim of this work is to get acquainted with the topic of quantum chaos and statistical methods used to quantify it. In the first part of this work I will show the definition of both classical and quantum chaos. I will introduce NNS method, which studies quantum chaos as correlations between levels in the spectrum. In the second part of my work I will describe basic methods used to work with data in a form of probability density. In the third part this work I will focus on methods that are specific for quantum chaos. To simulate a quantum chaotic system I will use the basics of random matrix theory. I will introduce unfolding and I will study the distribution of NNS for simulated spectra. To quantify quantum chaos I will use Brody distribution. In the last part of this work I will apply above mentioned methods on spectra of real particles.
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