Dissipation in mesoscopic quantum systems: Quantum friction and braiding in dissipative-driven Majorana boxes

This thesis explores two distinct yet interrelated areas of quantum physics: quantum friction in mesoscopic systems and topological quantum computing using Majorana bound states (MBSs). The work provides a comprehensive theoretical framework for understanding and potentially developing these applications in nanoscale quantum systems. The first part of this thesis investigate quantum friction, arising from the interaction with quantum vacuum fluctuations, which can generate forces between two parallel, neutral plates when they move relative to each other. This is a quantum mechanical effect analogous to the Casimir force but with a dynamic component due to the relative motion. Although quantum friction, like the Casimir effect, is expected to be a universal phenomenon, its direct observation has been elusive due to its extremely small magnitude and the complexities introduced by other quantum effects, such as spatial dispersion. Our contribution focuses on the phenomenon of quantum friction between plates in the hydrodynamic regime, where spatial dispersion—linked to the effective speed of sound in the material—cannot be ignored. In this context, quantum friction occurs only when the atom's velocity exceeds the material's effective sound speed. We provide analytical arguments to demonstrate that this result holds at all orders of perturbation theory. The second topic focuses on investigating braiding protocols within open systems based on the Majorana architecture, which consists of Majorana boxes or Cooper-pair box. These boxes are coupled to quantum dots with tunable tunneling parameters, and the entire system interacts with a large bosonic bath. Using the Lindblad formalism, we explore how the Majorana sector can be driven to specific designed steady states. In this framework, we assess the feasibility of non-Abelian braiding, which offers a potential route to fault-tolerant quantum computing. Finally, we provide a comprehensive guideline for the braiding protocols and the associated tunneling system.