The investigation of the phenomenon of dephasing assisted quantum transport, which happens when the presence of dephasing benefits the efficiency of this process, has been mainly focused on Markovian scenarios associated with constant and positive dephasing rates in their respective Lindblad master equations. What happens if we consider a more general framework, where time-dependent dephasing rates are allowed, thereby, permitting the possibility of non-Markovian scenarios? Does dephasing-assisted transport still manifest for non-Markovian dephasing? Here, we address these open questions in a setup of coupled two-level systems. Our results show that the manifestation of non-Markovian dephasing-assisted transport depends on the way in which the incoherent energy sources are locally coupled to the chain. This is illustrated with two different configurations, namely non-symmetric and symmetric. Specifically, we verify that non-Markovian dephasing-assisted transport manifested only in the non-symmetric configuration. This allows us to draw a parallel with the conditions in which time-independent Markovian dephasing-assisted transport manifests. Finally, we find similar results by considering a controllable and experimentally implementable system, which highlights the significance of our findings for quantum technologies.
Normal solutions for master equations with time-dependent transition rates: Application to heating processes