Open quantum systems (OQSs) cannot always be described with the Markov approximation,
which requires a large separation of system and environment time scales. An overview is …

Quantum dynamical maps provide suitable mathematical representation of quantum
evolutions. When representing quantum states by density operators, the evident …

We present a comprehensive and up-to-date review of the concept of quantum non-
Markovianity, a central theme in the theory of open quantum systems. We introduce the …

Discoveries in quantum materials, which are characterized by the strongly quantum-
mechanical nature of electrons and atoms, have revealed exotic properties that arise from …

The field of classical stochastic processes forms a major branch of mathematics. Stochastic
processes are, of course, also very well studied in biology, chemistry, ecology, geology …

To write an introduction to the dynamics of open quantum systems may seem at first a
complicated, albeit perhaps unnecessary, task. On the one hand, the field is quite broad and …

Bounds to the speed of evolution of a quantum system are of fundamental interest in
quantum metrology, quantum chemical dynamics, and quantum computation. We derive a …

Reinvigorated by advances and insights, in particular from the active fields of quantum
information and computing, the quantum theory of irreversible processes has recently …

Excitation transfer through interacting systems plays an important role in many areas of
physics, chemistry, and biology. The uncontrollable interaction of the transmission network …

We analyze two recently proposed measures of non-Markovianity: one based on the
concept of divisibility of the dynamical map and the other one based on distinguishability of …