Conservation law of operator current in open quantum systems

TL;DR

This paper establishes a fundamental conservation law for operator currents in open quantum systems and shows that common approximations like the secular approximation can violate this law, affecting the accuracy of quantum dynamics models.

Contribution

It derives a universal conservation law for operator currents and analyzes how certain approximations violate it, impacting the validity of master equations.

Findings

Secular approximation can break the conservation law.

Violations lead to artificial corrections in quantum dynamics.

The conservation law provides a criterion for assessing master equations.

Abstract

We derive a fundamental conservation law of operator current for master equations describing reduced quantum systems. If this law is broken, the temporal integral of the current operator of an arbitrary system observable does not yield in general the change of that observable in the evolution. We study Lindblad-type master equations as examples and prove that the application of the secular approximation during their derivation results in a violation of the conservation law. We show that generally any violation of the law leads to artificial corrections to the complete quantum dynamics, thus questioning the accuracy of the particular master equation.