Generalized quantum master equation from memory kernel coupling theory

TL;DR

This paper extends the Memory Kernel Coupling Theory to a tensorial framework, significantly improving the calculation of non-Markovian dynamics in open quantum systems with applications to various benchmark models.

Contribution

The paper introduces a tensorial extension to MKCT, enabling more accurate and efficient evaluation of memory kernels for complex quantum dynamics.

Findings

Accurately captures transient populations and coherences in the spin-boson model

Resolves the excitonic absorption spectrum of FMO complex

Simulates charge mobility in 1D lattice models efficiently

Abstract

The generalized quantum master equation provides a powerful framework for non-Markovian dynamics of open quantum systems. However, the accurate and efficient evaluation of the memory kernel remains a challenge. In this work, we introduce a comprehensive tensorial extension to the Memory Kernel Coupling Theory (MKCT) to overcome this bottleneck. By elevating the original scalar formalism to a tensorial framework, the extended MKCT enables the calculation of general expectation values and cross-correlation functions. We demonstrate the numerical accuracy and efficiency of this method across multiple benchmark systems: capturing transient populations and coherences in the spin-boson model, resolving the excitonic absorption spectrum of the Fenna-Matthews-Olson complex, and simulating charge mobility in one-dimensional lattice models. These successful applications establish the tensorial MKCT as a highly efficient tool for investigating complex dynamics in open quantum systems.