Quantum Transport in Mesoscopic Systems: a Non-Equilibrium Field Theory Approach

This thesis develops, extend, and applies a powerful framework, known as Keldysh field theory (KFT), to investigate quantum transport in mesoscopic systems out of equilibrium, with a particular focus on non-equilibrium steady states (NESS). This approach offers a versatile and efficient toolkit for studying transport properties, such as current and noise, in a wide range of mesoscopic setups. The thesis systematically applies this framework to a series of increasingly complex systems. First, quantum point contacts (QPCs), both normal and superconducting, are analyzed to benchmark the method against well-established results. Next, we explore quantum dots (QDs) connected to metallic and superconducting leads. Here, new insights are obtained into conductance behavior, particularly the role of level structure and interference effects, as well as into thermoelectric properties, including the conditions that optimize thermoelectric response. The final part of thework investigates transport through a more exotic model: a spinful version of the Sachdev-Ye-Kitaev (SYK) model with complex fermions coupled to normal metallic leads. This strongly interacting, non-Fermi liquid system has not yet been realized experimentally, and our analysis provides concrete predictions for its electric and thermoelectric response. Some of these results may offer guidance for future experimental efforts, highlighting specific signatures and regimes where unconventional physics is expected to emerge. This work is motivated by the fundamental importance of quantum transport processes for emerging quantum technologies and by the need to understand novel physical phenomena that arise in low-dimensional, strongly correlated systems. vii