The hierarchical and perturbative forms of stochastic Schr\"odinger equations and their applications to carrier dynamics in organic materials

TL;DR

This paper reviews non-Markovian stochastic Schr"odinger equations, from hierarchical to perturbative forms, highlighting their potential for modeling complex open quantum systems like organic materials and their applications in exciton dynamics and photovoltaics.

Contribution

It systematically connects various wavefunction-based approaches for open systems and demonstrates their application to organic material dynamics and energy transfer processes.

Findings

Demonstrated excitation energy transfer in Fenna-Matthews-Olson complex

Quantified decoherence timescales of hot excitons

Analyzed quantum interference in singlet fission processes

Abstract

A number of non-Markovian stochastic Schr\"odinger equations, ranging from the numerically exact hierarchical form towards a series of perturbative expressions sequentially presented in an ascending degrees of approximations are revisited in this short review, aiming at providing a systematic framework which is capable to connect different kinds of the wavefunction-based approaches for an open system coupled to the harmonic bath. One can optimistically expect the extensive future applications of those non-Markovian stochastic Schr\"odinger equations in large-scale realistic complex systems, benefiting from their favorable scaling with respect to the system size, the stochastic nature which is extremely suitable for parallel computing, and many other distinctive advantages. In addition, we have presented a few examples showing the excitation energy transfer in Fenna-Matthews-Olson complex, a quantitative measure of decoherence timescale of hot exciton, and the study of quantum interference effects upon the singlet fission processes in organic materials, since a deep understanding of both mechanisms is very important to explore the underlying microscopic processes and to provide novel design principles for highly efficient organic photovoltaics.