Markovian Repeated Interaction Quantum Systems

We study a class of dynamical semigroups (L)n∈N that emerge, by a Feynman–Kac type formalism, from a random quantum dynamical system (Lωn ◦ · · · ◦Lω1 (ρω0 ))n∈N driven by a Markov chain (ωn)n∈N. We show that the almost sure large time behavior of the system can be extracted from the large n asymptotics of the semigroup, which is in turn directly related to the spectral properties of the generator L. As a physical application, we consider the case where the Lω’s are the reduced dynamical maps describing the repeated interactions of a system S with thermal probes Eω. We study the full statistics of the entropy in this system and derive a fluctuation theorem for the heat exchanges and the associated linear response formulas.