On the hybrid Davies like generator for quantum dissipation

We provide a class of quantum evolution beyond Markovian semigroup. This is governed by hybrid Davies like generator such that dissipation controlled suitable memory kernel and decoherence standard GKLS generator. These two processes commute both them with the unitary systems Hamiltonian. The corresponding gives rise to semi-Markov diagonal elements density matrix. However, needs not be completely positive. role restore complete positivity. Hence, pose dynamical problem one generated classical purely scheme illustrated for qubit evolution.