Dynamics of single and many-body open quantum systems beyond the Markov approximation

Open quantum systems (OQS) cannot always be described with the Markov approximation, which requires a large separation of system and environment time scales. In this talk, I will give an overview of some of the most important techniques available to tackle the dynamics of an OQS beyond such Markov approximation. I will place special emphasis on methods based on solving the dynamics of both the system and its environment, and discuss some relevant applications where non-Markovian effects are important, such as atoms coupled to a one dimensional electromagnetic field. In addition, I will discuss the dynamics of non-correlated and strongly correlated many-body open systems, as well as the interplay between the system correlation strength and the dissipation.