Markovian treatment of non-Markovian dynamics of open Fermionic systems

Abstract

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.

Keywords

• Markov
• Lindblad
• open fermionic systems
• non-Markov dynamics
• AMEA
• dual fermion