Energy transfer in structured and unstructured environments: master equations beyond the Born-Markov approximations

TL;DR

This paper advances the modeling of excitonic energy transfer by extending the reaction coordinate master equation to include non-Markovian effects, demonstrating improved accuracy over traditional approaches in structured and unstructured environments.

Contribution

It develops a generalized reaction coordinate master equation that captures non-Markovian dynamics beyond Born-Markov approximations, validated against hierarchical equations of motion.

Findings

Accurate energy transfer dynamics in various environments.

Semiclassical Zusman equations often fail to capture quantum correlations.

Structured environments can enhance transfer rates depending on resonance conditions.

Abstract

We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed in [J. Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e. sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.