# Higher-order corrections to the Redfield equation with respect to the system-bath coupling based on the hierarchical equations of motion

## TL;DR

This paper develops a general method to derive higher-order corrections to the Redfield quantum master equation using hierarchical equations of motion, improving its accuracy for stronger system-bath couplings.

## Contribution

The authors introduce a novel approach based on HEOM to systematically obtain higher-order corrections to the Redfield equation, extending its applicability.

## Key findings

- Derived conditions for the validity of the Redfield equation.
- Established criteria for the secular approximation in open quantum systems.
- Provided a framework for more accurate modeling of system-bath interactions.

## Abstract

The Redfield equation describes the dynamics of a quantum system weakly coupled to one or more reservoirs and is widely used in theory of open quantum system. However, the assumption of weak system-reservoir coupling is often not fully adequate and higher-order corrections to the Redfield equation with respect to the system-bath coupling is required. Here we propose a general method of derivation of higher-order corrections to the Redfield quantum master equation based on the hierarchical equations of motion (HEOM). Also we derive conditions of validity of the Redfield equation as well as the additional secular approximation for it.