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Exact Generator and its High Order Expansions in Time-Convolutionless Generalized Master Equation: Applications to Spin-Boson Model and Exictation Energy Transfer
Yan-ying Liu,Ya-ming Yan,Meng Xu,Kai Song,Qiang Shi*
Author NameAffiliationE-mail
Yan-ying Liu Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China;University of Chinese Academy of Sciences, Beijing 100049, China  
Ya-ming Yan Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China;University of Chinese Academy of Sciences, Beijing 100049, China  
Meng Xu Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China;University of Chinese Academy of Sciences, Beijing 100049, China  
Kai Song Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China;University of Chinese Academy of Sciences, Beijing 100049, China  
Qiang Shi* Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, CAS Research/Education Center for Excellence in Molecular Sciences, Institute of Chemistry, Chinese Academy of Sciences, Beijing 100190, China;University of Chinese Academy of Sciences, Beijing 100049, China qshi@iccas.ac.cn 
Abstract:
The time-convolutionless (TCL) quantum master equation provides a powerful tool to simulate reduced dynamics of a quantum system coupled to a bath. The key quantity in the TCL master equation is the so-called kernel or generator, which describes effects of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present a new approach to calculating the exact TCL generator and its high order perturbative expansions. The new approach is applied to the spin-boson model with different sets of parameters, to investigate the convergence of the high order expansions of the TCL generator. We also discuss circumstances where the exact TCL generator becomes singular for the spin-boson model, and a model of excitation energy transfer in the Fenna-Matthews-Olson complex.
Key words:  Time-convolutionless generalized master equation  Spin-boson model  Exact generator  High order expansion
FundProject:This work is supported by the National Natural Science Foundation of China (No.21673246), and the Strategic Priority Research Program of the Chinese Academy of Sciences (No.XDB12020300).
时间无卷积广义主方程中核函数的精确解和高阶微扰展开:在自旋-玻色模型和激发态能量转移中的应用
柳燕莺,闫亚明,许猛,宋凯,史强*
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DOI:10.1063/1674-0068/31/cjcp1806146
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