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Recent years have seen tremendous progress in the theoretical understanding of quantum systems driven dissipatively by coupling them to different baths at their edges. This was possible because of the concurrent advances in the models used to represent these systems, the methods employed, and the analysis of the emerging phenomenology. Here we aim to give a comprehensive review of these three integrated research directions. We first provide an overarching view of the models of boundary driven open quantum systems, both in the weak and strong coupling regimes. This is followed by a review of state-of-the-art analytical and numerical methods, both exact, perturbative and approximate. Finally, we discuss the transport properties of some paradigmatic one-dimensional chains, with an emphasis on disordered and quasiperiodic systems, the emergence of rectification and negative differential conductance, and the role of phase transitions.
We investigate the steady state properties arising from the open system dynamics described by a memoryless (Markovian) quantum collision model, corresponding to a master equation in the ultra-strong coupling regime. By carefully assessing the work co
We propose a fully operational framework to study the non-equilibrium thermodynamics of a quantum system $S$ that is coupled to a detector $D$ whose state is continuously monitored, allowing to single out individual quantum trajectories of $S$. We fo
The unitary dynamics of isolated quantum systems does not allow a pure state to thermalize. Because of that, if an isolated quantum system equilibrates, it will do so to the predictions of the so-called diagonal ensemble $rho_{DE}$. Building on the i
A universal scheme is introduced to speed up the dynamics of a driven open quantum system along a prescribed trajectory of interest. This framework generalizes counterdiabatic driving to open quantum processes. Shortcuts to adiabaticity designed in t
Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a fi