Non-Markovian dynamics of open quantum systems

Quantum systems existing in laboratories or other physical realms are usually far of being isolated as their dynamics is affected by background noise, and the information from there is lost due to parasitic interactions with the surrounding world. Such systems are called open quantum systems (OQS), and the degrees of freedom affecting their dynamics are collectively called the environment. For the description of the dynamics of the open quantum system without the knowledge of the state of the environment, there exists a master equation, which is usually used in the Lindblad form. Several approximations are used in the derivation of the Lindblad equation, among which are the separability of initial states of the system and the environment, negligible relaxation time of the environment in comparison with characteristic timescales of OQS evolution, and the Markov assumption, which physical meaning is the absence of memory effects in the system dynamics. The development of a formalism for describing processes occurring in quantum systems outside of these approximations and of the mathematical definition of non-Markovian dynamics has attracted increased interest in the last decade. Despite remarkable progress in the field, there are still many questions that remain unclear.