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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 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 two-level atoms and a single-mode bosonic field (schematic model for cavity quantum electrodynamics). The model belongs to the class of so-called 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 ground-state quantum phase transitions (QPTs) and the excited-state 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 atom-field 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 non-integrable perturbation is observed. The dynamical consequences of the ESQPTs are examined using quantum quenches. The influence of the...
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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 Wichmann-Kroll 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 self-energy 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 ground-state en- ergy splitting due to the tunneling in a two-dimensional double-well 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
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