Regularizations and exact methods for non-Markovian open quantum systems

Any realistic physical object ought to be regarded as open to influences from an external uncontrollable environment. Consequently, one of the main topics in the theory of open quantum systems is to derive expressive dynamical laws—master equations—from a microscopic description of the system-environment compound. While plenty has been said in the Markovian regime, where there is a unilateral flow of information from the system to the environment, much less is known beyond it. In this thesis we discuss new techniques to address situations framed in the non-Markovian phenomenology. First, we propose two state- of-art methods to regularize master equations affected by the issue of positivity breaking: such phenomenon is known to occur after weak-coupling expansions, with the celebrated Redfield equation being the primary example of defective occurrence. Then, in order to make progress in the opposite strong-coupling scenario, we discuss methods that are applicable under certain Gaussianity assumptions. Adopting a fruitful marriage between the language of master equations and the Schwinger-Keldysh contour idea from many-body physics, we are able to construct exact stochastic and deterministic master equations with an unprecedented degree of generality and relative simplicity and intuitiveness.