Quantum-to-Classical Reduction of Quantum Master Equations

TL;DR

This paper introduces a quantum-to-classical reduction method for quantum master equations using a similarity transformation of the Liouvillian, addressing issues with the rotating wave approximation and enabling classical calculations of quantum transport.

Contribution

The authors develop a novel reduction technique that transforms quantum dynamics into classical equations, providing a more accurate and physically consistent approach.

Findings

The method clarifies why the rotating wave approximation can be unphysical.

It allows exact replacement of quantum dynamics with classical equations.

The approach improves calculations of quantum transport efficiency.

Abstract

A general method of quantum-to-classical reduction of quantum dynamics is described. The key aspect of our method is the similarity transformation of the Liouvillian, which provides a new perspective. In conventional studies of quantum energy transport, the rotating wave approximation has been frequently regarded as an inappropriate approach because it causes the energy flow through the system to vanish. Our formulation elucidates as to why this unphysical result occurs and provides a solution for the problem. That is, not only the density matrix but also the physical quantity is to be transformed. Moreover, we show that quantum dynamics can be "exactly" replaced with classical equations for the calculation of the transport efficiency.