Open extended quantum systems

We present an introduction to the theory of open extended quantum systems. We begin with a microscopic derivation of the so-called Lindblad equation followed by a more abstract approach. Next, we introduce collision models, a versatile framework that offers a possible unraveling of the non-unitary dynamics of open quantum systems. We finally discuss concrete situations involving quantum transport phenomena, the generation and replication of entanglement or even the non-thermal relaxation of cold atomic gases confined in optical traps.