Josephson effect in quantum dotsAlić, Amina (Avtor) Žitko, Rok (Mentor) Quantum dotsBCS superconductorsJosephson effectAndreev bound statesAndreev reflectionIn this master's thesis, I am considering the problem of two superconducting electrodes connected by a weak link. In such systems, a phenomenon known as the Josephson effect occurs. The Josephson effect is the flow of the direct electrical current through the non-biased system or the flow of the alternating current through the system which is biased by a constant voltage. That current is called the Josephson current and systems like those are known as Josephson junctions. In this thesis, the weak link between the superconducting electrodes consists of one or two quantum dots. In such cases, the Josephson current is carried by the discrete states known as Andreev bound states, formed through the Andreev reflection mechanism: electrons impinging on the interface between the superconductor and the normal metal are reflected back into the normal metal as holes, while pairs of electrons (the Cooper pairs) are formed in the superconductor. The Andreev bound states are visible as resonant peaks in the density of states of quantum dots. Here I search for those states in three different approximations: the case of no Coulomb repulsion between electrons in the dots, the case of electrons interacting through an infinite interaction and the case of infinite superconducting gap.20182018-09-26 07:45:17Magistrsko delo/naloga103788sl