Boson and Fermion Brownian Motion

TL;DR

This paper introduces a definition for fermion quantum Brownian motion, expanding the existing framework which was previously limited to boson systems, thus enabling the study of fermionic quantum stochastic processes.

Contribution

The paper provides a new definition for fermion quantum Brownian motion, complementing the existing boson-based models and broadening the scope of quantum stochastic differential equations.

Findings

Defined fermion quantum Brownian motion

Extended quantum stochastic differential equations to fermions

Facilitated analysis of fermionic quantum systems

Abstract

Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). To work it out one needs definition of quantum Brownian motion. Since till very recent times only its boson version has been known, in present paper we demonstrate definition which makes possible consideration also for fermion Brownian motion.