General Framework for Quantifying Dissipation Pathways in Open Quantum Systems. II. Numerical Validation and the Role of Non-Markovianity

TL;DR

This paper validates a Markovian decomposition method for energy dissipation in open quantum systems, showing that incorporating non-Markovian effects via time scale separations improves accuracy and computational efficiency.

Contribution

The paper introduces a method combining MQME-D with time scale separations to accurately quantify dissipation pathways, including non-Markovian effects, with reduced computational cost.

Findings

MQME-D accurately predicts bath contributions to dissipation.

Incorporating non-Markovianity via TSS enhances accuracy.

The combined approach is computationally efficient for realistic systems.

Abstract

In the previous paper [C. W. Kim and I. Franco, J. Chem. Phys. 160, 214111 (2024)], we developed a theory called MQME-D, which allows us to decompose the overall energy dissipation process in open quantum system dynamics into contributions by individual components of the bath when the subsystem dynamics is governed by a Markovian quantum master equation (MQME). Here, we contrast the predictions of MQME-D against the numerically exact results obtained by combining hierarchical equations of motion (HEOM) with a recently reported protocol for monitoring the statistics of the bath. Overall, MQME-D accurately captures the contributions of specific bath components to the overall dissipation while greatly reducing the computational cost as compared to exact computations using HEOM. The computations show that MQME-D exhibits errors originating from its inherent Markov approximation. We demonstrate that its accuracy can be significantly increased by incorporating non-Markovianity by exploiting time scale separations (TSS) in different components of the bath. Our work demonstrates that MQME-D combined with TSS can be reliably used to understanding how energy is dissipated in realistic open quantum system dynamics.