Nonequilibrium boundary-driven quantum systems: Models, methods, and properties

Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling to different baths at their edges. This was possible because of concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. A comprehensive review of these three integrated research directions is given. First provided is an overarching view of the models of boundary-driven open quantum systems, in both the weak-and strong-coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods that are exact, perturbative, and approximate. Finally, the transport properties of some paradigmatic one-dimensional chains are discussed, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions, and an outlook on further research options is given.

Automated summary

Recent years have witnessed significant progress in the theoretical understanding of quantum systems driven dissipatively by coupling to different baths. This progress has been possible due to advancements in models, methods, and analysis of emerging phenomena. This review provides a comprehensive overview of these three integrated research directions. It first gives an overarching view of boundary-driven open quantum system models in both weak and strong coupling regimes. It then reviews state-of-the-art analytical and numerical methods that are exact, perturbative, and approximate. Lastly, it discusses transport properties of paradigmatic one-dimensional chains, with a focus on disordered and quasiperiodic systems, rectification and negative differential conductance, phase transitions, and provides an outlook on further research options.