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.
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August 2018
Research Article|
August 01 2018
Exact generator and its high order expansions in time-convolutionless generalized master equation: Applications to spin-boson model and excitation energy transfer†
Yan-ying Liu;
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
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Ya-ming Yan;
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
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Meng Xu;
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
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Kai Song;
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
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Qiang Shi
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
*Author to whom Correspondence should be addressed. E-mail: [email protected]
Search for other works by this author on:
Yan-ying Liu
,
Ya-ming Yan
,
Meng Xu
,
Kai Song
,
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
*Author to whom Correspondence should be addressed. E-mail: [email protected]
†
Part of the special issue for celebration of “the 60th Anniversary of University of Science and Technology of China and the 30th Anniversary of Chinese Journal of Chemical Physics”.
Chin. J. Chem. Phys. 31, 575–583 (2018)
Article history
Received:
June 20 2018
Accepted:
July 27 2018
Citation
Yan-ying Liu, Ya-ming Yan, Meng Xu, Kai Song, Qiang Shi; Exact generator and its high order expansions in time-convolutionless generalized master equation: Applications to spin-boson model and excitation energy transfer. Chin. J. Chem. Phys. 1 August 2018; 31 (4): 575–583. https://doi.org/10.1063/1674-0068/31/cjcp1806146
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