Different types of open quantum systems evolving in a Markovian regime
  The interaction between an open quantum system and its environment induces generally memory effects generated by the fact that the response of the system to the environment is not instantaneous. Different physical reasons can be at the origin of an absence of time retardation. We present here a study of systems for which instantaneouness is realized although they do not necessarily follow established Markovian criteria. 
Tarek Khalil and Jean Richert
quant-ph