Comparison of non-Markovianity criteria in a qubit system under random external fields

We give the map representing the evolution of a qubit under the action of non-dissipative random external fields. From this map, we construct the corresponding master equation that in turn allows us to phenomenologically introduce population damping of the qubit system. We then compare, in this system, the time regions where non-Markovianity is present on the basis of different criteria for both the non-dissipative and the dissipative case. We show that the adopted criteria agree both in the non-dissipative case and in the presence of population damping.