Gebonden Toestanden en Stromen

This thesis comprises a wide range of topics. The first work revolves around an active matter system, where a bound state between two run-and-tumble probe particles is induced by a thermal medium, whose interactions with the probe are purely repulsive. The bound state is then induced by the self-trapping behavior of the active particles and the density profile of the thermal particles. There is a surprising analogy between the formation of these bound states and the formation of Cooper pairs in superconductors. The electron, as described by the Dirac equation, may be seen as obeying a master equation of precisely the same form as the master equation of the run-and-tumble particle. Taking this view literally, Cooper pairs are bound states of two run-and-tumble particles whose binding is enabled by the thermal medium in which they reside. The second chapter revolves around these zig-zag electrons which are described by this master-equation formulation of the Dirac equation. This zig-zag behavior may be visualized by the calculation of trajectories that form an extension of Bohmian trajectories. These tools of visualization are then applied to the famous Stern-Gerlach experiment. The third part of the thesis concerns superconductivity, and more specifically the Josephson effect. Josephson junctions form the cornerstone of superconducting quantum technology, providing anharmonicity to qubits and phase sensitivity to SQUIDs. The physics of Josephson junctions is very rich, with features such as Andreev bound states playing a crucial part in the understanding of the Josephson current and the current-phase relation. Yet the microscopic modeling of Josephson junctions remains challenging, and many things remain unexplained. One of the issues addressed in this thesis is the issue of current conservation in the modeling of Josephson junctions, but also in mean-field superconductivity generally. We show that ensuring current conservation has a dramatic effect on the Andreev states and on the current-phase relation, challenging assumptions which have long become standard in the literature. The final part of the thesis is concerned with superconducting qubits, and the effect of the precise shape of the CPR on qubit properties. We uncover resonances of the Andreev bound states, and show that these resonances correspond to lessened anharmonicity for transmon qubits.