Markovian Treatment of non-Markovian Dynamics of Open Fermionic Systems

TL;DR

This paper presents an exact mapping of open fermionic systems interacting with a continuous environment onto an auxiliary system with discrete modes, enabling easier analysis of their dynamics and extending previous Bose system work.

Contribution

It introduces a novel exact mapping technique for open fermionic systems to a Lindblad-type model, extending prior Bose system methods to Fermi systems and multi-time correlations.

Findings

Exact mapping between continuous environment and discrete modes

Conditions for equivalence of reduced dynamics established

Numerical simulations demonstrate the approach's effectiveness

Abstract

We show that an open fermionic system coupled to 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. The study is extension of recent work on Bose systems [D. Tamascelli, A. Smirne, S. F. Huelga, and M. B. Plenio, Phys. Rev. Lett. 120, 030402 (2018)] to open quantum Fermi systems and to multi-time correlation functions. Numerical simulations within generic junction model are presented for illustration.