Markovian treatment of non-Markovian dynamics of open Fermionic systems

We show that an open fermionic system coupled to a continuous environment with unitary system-environment evolution can be exactly mapped onto an auxiliary system consisting of the physical fermion system and a set of discrete fermionic modes subject to non-unitary Lindblad-type system-modes evolution in such a way that reduced dynamics of the fermionic system in the two cases are the same. Conditions for equivalence of reduced dynamics in the two systems are identified and a proof is presented. Our study extends recent work on Bose systems (Tamascelli et al 2018 Phys. Rev. Lett. 120 030402) to the case of open quantum Fermi systems and to multi-time correlation functions. Numerical simulations within a generic junction model are presented for illustration.