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Quantum electronic transport in superconducting quantum dots
Kadlecová, Alžběta ; Novotný, Tomáš (advisor) ; Kos, Šimon (referee) ; Munzar, Dominik (referee)
In this thesis, the single-level correlated quantum dot attached to two BCS superconducting leads is analyzed. A difference in the superconducting phases of the leads induces the DC Josephson supercurrent in the junction. In this setup, the influence of asymmetrical dot-lead couplings on transport properties is clarified analytically. The coupling asymmetry and the phase difference can be combined into one function, which allows us to calculate physical properties of a system with coupling asymmetry from the properties of its effective symmetric counterpart. The coupling asymmetry turns out to be an important parameter which influences the position of the 0 − � quantum phase transition even in the strongly correlated Kondo regime. Further, this thesis contributes to the interpretation of an AC Josephson current measurement, in which a surprising drop in the amplitude was observed in the Kondo regime. The experimental setup is characterized using numerical renormalization group calculations of the equilibrium many-body spectra. Possible quantum-point-contact- based interpretations are discussed. Although a drop in the AC Josephson current at the experimental bias voltage is also expected in a quantum point contact, we conclude that the physical mechanisms causing it in the quantum dot system are likely not...
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Gravitational waves in cosmology
Kadlecová, Alžběta ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
In this work, we study the backreaction of high-frequency gravitational waves on cosmological backgrounds. To describe the wave, we use the Isa- acson formalism, specifically the WKB approximation, which allows us to express the backreaction through an effective stress-energy tensor of the gra- vitational wave. First, we consider the inhomogeneous cosmological model of Charach and Malin, which contains gravitational waves and a massless scalar field mini- mally coupled to gravity. We show that although this is a spatially compacti- fied solution, it is possible to add a high-frequency perturbation and solve Einstein's equations with the effective stress-energy tensor in a consistent way. The bacreaction is of the same order as the influence of the scalar field. Second, we add multiple incoherent high-frequency waves to the homoge- neous Kasner background, and discuss the relation to the late-time limit of the Gowdy (vacuum Charach and Malin) model. 1
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