Modified quantum regression theorem and consistency with Kubo-Martin-Schwinger condition

TL;DR

This paper introduces a modified quantum regression theorem that ensures consistency with the Kubo-Martin-Schwinger condition in open quantum systems, improving accuracy over the standard theorem in certain models.

Contribution

The authors develop a new version of the quantum regression theorem using a Heisenberg operator approach and a weak Markov approximation, ensuring KMS condition compliance.

Findings

Modified theorem respects KMS condition at non-zero system-bath coupling

Predicts exact results for specific models in certain limits

Outperforms the standard quantum regression theorem when discrepancies occur

Abstract

We show that the long-time limit of the two-point correlation function obtained via the standard quantum regression theorem, a standard tool to compute correlation functions in open quantum systems, does not respect the Kubo-Martin-Schwinger equilibrium condition to the non-zero order of the system-bath coupling. We then follow the recently developed Heisenberg operator method for open quantum systems and by applying a ``{\it weak}" Markov approximation, derive a new modified version of the quantum regression theorem that not only respects the KMS condition but further predicts exact answers for certain paradigmatic models in specific limits. We also show that in cases where the modified quantum regression theorem does not match with exact answers, it always performs better than the standard quantum regression theorem.