微扰形式非马尔可夫随机薛定谔方程及其应用

Perturbative non-Markovian stochastic Schr dinger equations and their applications

近年来,越来越多的实验结果表明量子效应在各类光电材料超快动力学过程中有着非常重要的作用,对这些现象的理论研究促进了许多量子动力学方法的快速发展.和量子主方程相比,非马尔可夫随机薛定谔方程(non-Markovian stochastic Schr dinger equation,NMSSE)通过演化希尔伯特空间中的随机波函数求解动力学,其计算成本与系统大小之间具有良好的标度关系,适合进行高效的并行计算,因而在大尺度系统中受到广泛应用.本文主要介绍近年来本课题组针对大尺度开放量子系统所发展的微扰形式的NMSSE方法,从影响泛函框架出发回顾了微扰形式NMSSE的理论基础,讨论了其在不同表象下的形式和优缺点,并以有机体系中激子能量弛豫过程的模拟及载流子迁移率的计算为例阐述其应用.

In recent years,an increasing number of experiments have confirmed the crucial role played by quantum effects in the ultrafast dynamics of various optoelectronic materials,and theoretical research on these phenomena has boosted the rapid development of numerous quantum dynamics methods.Compared with quantum master equations,non-Markovian stochastic Schr dinger equations(NMSSEs)solve the dynamics with evolving stochastic wavefunctions in Hilbert space,and have been generally applied to large-scale systems due to their favorable scaling property with respect to the system size and the suitability of highly efficient parallel computing.Thispaper mainly focuses on perturbative NMSSEs developed for large-scale open quantum systems in recent years.The theoretical foundation of perturbative NMSSEs is revisited within the influence functional framework,and concrete expressions of perturbative NMSSEs as well as their merit and demerit in different representations,are discussed.To expound their applications,the simulation of the hot exciton energy relaxation process and the calculation of carrier mobilities in organic systems are presented as examples.