Classical and Quantum Part of the Environment for Quantum Langevin Equations

TL;DR

This paper characterizes quantum Langevin equations driven by classical noises and shows that any such equation can be decomposed into classical and quantum parts, providing a clear algebraic criterion.

Contribution

It offers a complete algebraic characterization of quantum Langevin equations driven by classical noises and demonstrates their decomposition into classical and quantum components.

Findings

Characterization of quantum Langevin equations driven by classical noises

Proof that any quantum Langevin equation can be split into classical and quantum parts

Algebraic criteria for identifying classical noise-driven equations

Abstract

Among quantum Langevin equations describing the unitary time evolution of a quantum system in contact with a quantum bath, we completely characterize those equations which are actually driven by classical noises. The characterization is purely algebraic, in terms of the coefficients of the equation. In a second part, we consider general quantum Langevin equations and we prove that they can always be split into a maximal part driven by classical noises and a purely quantum one.