Non-Markovian Fermionic Stochastic Schr\"{o}dinger Equation for Open System Dynamics

TL;DR

This paper introduces an exact Grassmann stochastic Schr"{o}dinger equation for open fermionic systems, enabling precise modeling of their dynamics and decoherence effects in various reservoir conditions.

Contribution

It presents a novel stochastic approach for fermionic open systems, deriving exact master equations and analyzing environment memory effects on quantum coherence.

Findings

Quantum coherence can be significantly affected by environment memory.

The approach applies to both vacuum and finite-temperature fermionic reservoirs.

Exact dynamics are obtained for systems strongly coupled to electronic reservoirs.

Abstract

In this paper we present an exact Grassmann stochastic Schr\"{o}dinger equation for the dynamics of an open fermionic quantum system coupled to a reservoir consisting of a finite or infinite number of fermions. We use this stochastic approach to derive the exact master equation for a fermionic system strongly coupled to electronic reservoirs. The generality and applicability of this Grassmann stochastic approach is justified and exemplified by several quantum open system problems concerning quantum decoherence and quantum transport for both vacuum and finite-temperature fermionic reservoirs. We show that the quantum coherence property of the quantum dot system can be profoundly modified by the environment memory.