Fermionic Stochastic Schr\"{o}dinger Equation and Master Equation: An Open System Model

TL;DR

This paper develops an exact fermionic stochastic Schr"{o}dinger equation and master equation for open quantum systems strongly coupled to fermionic baths, enabling detailed analysis of non-Markovian dynamics and bath effects.

Contribution

It introduces a fermionic quantum state diffusion approach derived from first principles, extending stochastic methods to fermionic environments and providing exact equations for open system dynamics.

Findings

Derived an exact fermionic QSD equation using fermionic coherent states.

Applied the approach to various models including qubits and fermionic systems.

Discussed differences in dynamics between fermionic and bosonic baths.

Abstract

This paper considers the extension of the non-Markovian stochastic approach for quantum open systems strongly coupled to a fermionic bath, to the models in which the system operators commute with the fermion bath. This technique can also be a useful tool for studying open quantum systems coupled to a spin-chain environment, which can be further transformed into an effective fermionic bath. We derive an exact stochastic Schr\"{o}dinger equation (SSE), called fermionic quantum state diffusion (QSD) equation, from the first principle by using the fermionic coherent state representation. The reduced density operator for the open system can be recovered from the average of the solutions to the QSD equation over the Grassmann-type noise. By employing the exact fermionic QSD equation, we can derive the corresponding exact master equation. The power of our approach is illustrated by the applications of our stochastic approach to several models of interest including the one-qubit dissipative model, the coupled two-qubit dissipative model, the quantum Brownian motion model and the N-fermion model coupled to a fermionic bath. Different effects caused by the fermionic and bosonic baths on the dynamics of open systems are also discussed.