Input and output in damped quantum systems III: Formulation of damped systems driven by Fermion fields

TL;DR

This paper develops a comprehensive input-output theory for Fermionic quantum systems, formulating quantum stochastic differential equations that account for anticommutation relations, advancing the understanding of damped Fermionic systems.

Contribution

It introduces a formalism for Fermionic input-output theory that incorporates anticommutation relations, extending quantum stochastic calculus to Fermionic systems.

Findings

Formulation of Fermionic quantum stochastic differential equations

Development of Ito and Stratonovich forms for Fermionic systems

Framework for analyzing damped Fermionic quantum systems

Abstract

A comprehensive input-output theory is developed for Fermionic input fields. Quantum stochastic differential equations are developed in both the Ito and Stratonovich forms. The major technical issue is the development of a formalism which takes account of anticommutation relations between the Fermionic driving field and those system operators which can change the number of Fermions within the system.