2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170478We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow the treatment of a variety of physical systems, as is illustrated by means of various examples and applications, including quantum optical systems and models of quantum transport.4 pages, revtex, no figures, to appear in Phys. Rev. LettQuantum PhysicsMathematical Physicstext