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Huang Z, Xu L, Zhou Z. Stochastic Schrödinger Equation Approach to Real-Time Dynamics of Anderson-Holstein Impurities: An Open Quantum System Perspective. J Chem Theory Comput 2024; 20:946-962. [PMID: 38194479 DOI: 10.1021/acs.jctc.3c01099] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2024]
Abstract
We develop a stochastic Schrödinger equation (SSE) framework to simulate the real-time dynamics of Anderson-Holstein (AH) impurities coupled to a continuous Fermionic bath. The bath degrees of freedom are incorporated through fluctuating terms determined by exact system-bath correlations, which is derived in an ab initio manner. We show that such an SSE treatment provides a middle ground between numerically expansive microscopic simulations and macroscopic master equations. Computationally, the SSE model enables efficient numerical methods for propagating stochastic trajectories. We demonstrate that this approach not only naturally provides microscopically detailed information unavailable from reduced models but also captures effects beyond master equations, thus serving as a promising tool to study open quantum dynamics emerging in physics and chemistry.
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Affiliation(s)
- Zhen Huang
- Department of Mathematics, University of California, Berkeley, California 94720, United States
| | - Limin Xu
- Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China
| | - Zhennan Zhou
- Beijing International Center for Mathematical Research, Peking University, Beijing 100871, China
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2
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Dan X, Xu M, Yan Y, Shi Q. Generalized master equation for charge transport in a molecular junction: Exact memory kernels and their high order expansion. J Chem Phys 2022; 156:134114. [PMID: 35395901 DOI: 10.1063/5.0086663] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive a set of generalized master equations (GMEs) to study charge transport dynamics in molecular junctions using the Nakajima-Zwanzig-Mori projection operator approach. In the new GME, time derivatives of population on each quantum state of the molecule, as well as the tunneling current, are calculated as the convolution of time non-local memory kernels with populations on all system states. The non-Markovian memory kernels are obtained by combining the hierarchical equations of motion (HEOM) method and a previous derived Dyson relation for the exact kernel. A perturbative expansion of these memory kernels is then calculated using the extended HEOM developed in our previous work [M. Xu et al., J. Chem. Phys. 146, 064102 (2017)]. By using the resonant level model and the Anderson impurity model, we study properties of the exact memory kernels and analyze convergence properties of their perturbative expansions with respect to the system-bath coupling strength and the electron-electron repulsive energy. It is found that exact memory kernels calculated from HEOM exhibit short memory times and decay faster than the population and current dynamics. The high order perturbation expansion of the memory kernels can give converged results in certain parameter regimes. The Padé and Landau-Zener resummation schemes are also found to give improved results over low order perturbation theory.
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Affiliation(s)
- Xiaohan Dan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and 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, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming Yan
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and 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, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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Lai Y, Geva E. On simulating the dynamics of electronic populations and coherences via quantum master equations based on treating off-diagonal electronic coupling terms as a small perturbation. J Chem Phys 2021; 155:204101. [PMID: 34852488 DOI: 10.1063/5.0069313] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum master equations provide a general framework for describing the dynamics of electronic observables within a complex molecular system. One particular family of such equations is based on treating the off-diagonal coupling terms between electronic states as a small perturbation within the framework of second-order perturbation theory. In this paper, we show how different choices of projection operators, as well as whether one starts out with the time-convolution or the time-convolutionless forms of the generalized quantum master equation, give rise to four different types of such off-diagonal quantum master equations (OD-QMEs), namely, time-convolution and time-convolutionless versions of a Pauli-type OD-QME for only the electronic populations and an OD-QME for the full electronic density matrix (including both electronic populations and coherences). The fact that those OD-QMEs are given in terms of the interaction picture makes it non-trivial to obtain Schrödinger picture electronic coherences from them. To address this, we also extend a procedure for extracting Schrödinger picture electronic coherences from interaction picture populations recently introduced by Trushechkin in the context of time-convolutionless Pauli-type OD-QME to the other three types of OD-QMEs. The performance of the aforementioned four types of OD-QMEs is explored in the context of the Garg-Onuchic-Ambegaokar benchmark model for charge transfer in the condensed phase across a relatively wide parameter range. The results show that time-convolution OD-QMEs can be significantly more accurate than their time-convolutionless counterparts, particularly in the case of Pauli-type OD-QMEs, and that rather accurate Schrödinger picture coherences can be obtained from interaction picture electronic inputs.
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Affiliation(s)
- Yifan Lai
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, USA
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4
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Jang SJ. Fourth order expressions for the electronic absorption lineshape of molecular excitons. J Chem Phys 2019; 151:044110. [DOI: 10.1063/1.5100986] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Seogjoo J. Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
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Gong Z, Wu J. Quantum kinetic expansion in the spin-boson model: Implemented by the quantum-classical Liouville equation in an anharmonic bath. J Chem Phys 2018; 148:234107. [DOI: 10.1063/1.5028306] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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Xu M, Yan Y, Liu Y, Shi Q. Convergence of high order memory kernels in the Nakajima-Zwanzig generalized master equation and rate constants: Case study of the spin-boson model. J Chem Phys 2018; 148:164101. [DOI: 10.1063/1.5022761] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- 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, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yaming 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, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Yanying 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, Zhongguancun, Beijing 100190, China and 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, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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Gong Z, Tang Z, Wang H, Wu J. Quantum kinetic expansion in the spin-boson model: Matrix formulation and system-bath factorized initial state. J Chem Phys 2017; 147:244112. [PMID: 29289122 DOI: 10.1063/1.4998784] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Within the framework of the hierarchy equation of motion (HEOM), the quantum kinetic expansion (QKE) method of the spin-boson model is reformulated in the matrix representation. The equivalence between the two formulations (HEOM matrices and quantum operators) is numerically verified from the calculation of the time-integrated QKE rates. The matrix formulation of the QKE is extended to the system-bath factorized initial state. Following a one-to-one mapping between HEOM matrices and quantum operators, a quantum kinetic equation is rederived. The rate kernel is modified by an extra term following a systematic expansion over the site-site coupling. This modified QKE is numerically tested for its reliability by calculating the time-integrated rate and non-Markovian population kinetics. For an intermediate-to-strong dissipation strength and a large site-site coupling, the population transfer is found to be significantly different when the initial condition is changed from the local equilibrium to system-bath factorized state.
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Affiliation(s)
- Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Zhoufei Tang
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Haobin Wang
- Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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Xu M, Song L, Song K, Shi Q. Convergence of high order perturbative expansions in open system quantum dynamics. J Chem Phys 2017; 146:064102. [DOI: 10.1063/1.4974926] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Meng Xu
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
| | - Linze Song
- Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and 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, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and 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, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190, China and University of Chinese Academy of Sciences, Beijing 100049, China
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9
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Chen HT, Berkelbach TC, Reichman DR. On the accuracy of the Padé-resummed master equation approach to dissipative quantum dynamics. J Chem Phys 2016; 144:154106. [DOI: 10.1063/1.4946809] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hsing-Ta Chen
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
| | - Timothy C. Berkelbach
- Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
| | - David R. Reichman
- Department of Chemistry, Columbia University, 3000 Broadway, New York, New York 10027, USA
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Tang Z, Gong Z, Wu J. Generalized quantum kinetic expansion: Time scale separation between intra-cluster and inter-cluster kinetics. J Chem Phys 2015; 143:104107. [DOI: 10.1063/1.4930012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Affiliation(s)
- Zhoufei Tang
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Zhihao Gong
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
| | - Jianlan Wu
- Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China
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12
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Mavros MG, Van Voorhis T. Resummed memory kernels in generalized system-bath master equations. J Chem Phys 2014; 141:054112. [DOI: 10.1063/1.4891669] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michael G. Mavros
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, Massachusetts 02139, USA
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Li L, Giokas PG, Kanai Y, Moran AM. Modeling time-coincident ultrafast electron transfer and solvation processes at molecule-semiconductor interfaces. J Chem Phys 2014; 140:234109. [DOI: 10.1063/1.4882664] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Abstract
For a quantum system interacting with its environment, the role of state preparation is nontrivial. The reason is that before the state preparation procedure, the system and the environment are correlated. Consequently, the state preparation procedure (which acts on the system) indirectly influences the state of the environment depending on the state preparation. In this paper, we use an experimentally realizable model describing a collection of N two-level atoms coupled to a common environment to investigate the influence of the state preparation procedure. We show that the dynamical map describing the evolution of the open quantum system can depend appreciably on the state preparation procedure. Moreover, this effect can be enhanced by increasing N. Our results should be useful for quantum control and quantum tomography.
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Affiliation(s)
- Adam Zaman Chaudhry
- NUS Graduate School for Integrative Sciences and Engineering, Singapore 117597, Singapore
| | - Jiangbin Gong
- NUS Graduate School for Integrative Sciences and Engineering, Singapore 117597, Singapore
- Department of Physics and Center for Computational Science and Engineering, National University of Singapore, Singapore 117542, Singapore
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15
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Asplund E, Klüner T. A Surrogate Hamiltonian study of femtosecond photodesorption of CO from NiO(100). Mol Phys 2013. [DOI: 10.1080/00268976.2013.813589] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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16
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Cook WR, Coalson RD, Evans DG. Effectiveness of Perturbation Theory Approaches for Computing Non-Condon Electron Transfer Dynamics in Condensed Phases. J Phys Chem B 2009; 113:11437-47. [DOI: 10.1021/jp9007976] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Affiliation(s)
- William R. Cook
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, and Department of Chemistry, University of Pittsburgh, Pennsylvania 15260
| | - Rob D. Coalson
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, and Department of Chemistry, University of Pittsburgh, Pennsylvania 15260
| | - Deborah G. Evans
- Department of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131, and Department of Chemistry, University of Pittsburgh, Pennsylvania 15260
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Shi Q, Geva E. A self-consistent treatment of electron transfer in the limit of strong friction via the mixed quantum classical Liouville method. J Chem Phys 2009; 131:034511. [DOI: 10.1063/1.3176509] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
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18
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Abstract
We review recent theoretical and experimental advances in the elucidation of the dynamics of light harvesting in photosynthesis, focusing on recent theoretical developments in structure-based modeling of electronic excitations in photosynthetic complexes and critically examining theoretical models for excitation energy transfer. We then briefly describe two-dimensional electronic spectroscopy and its application to the study of photosynthetic complexes, in particular the Fenna-Matthews-Olson complex from green sulfur bacteria. This review emphasizes recent experimental observations of long-lasting quantum coherence in photosynthetic systems and the implications of quantum coherence in natural photosynthesis.
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Affiliation(s)
- Yuan-Chung Cheng
- Department of Chemistry and QB3 Institute, University of California, Berkeley and Physical Bioscience Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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Nan G, Shi Q, Shuai Z. Nonperturbative time-convolutionless quantum master equation from the path integral approach. J Chem Phys 2009; 130:134106. [DOI: 10.1063/1.3108521] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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20
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Song X, Wang H, Van Voorhis T. A Langevin equation approach to electron transfer reactions in the diabatic basis. J Chem Phys 2008; 129:144502. [DOI: 10.1063/1.2991294] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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Golosov AA, Reichman DR. Critical tests of a new master equation approach to nonadiabatic quantum dissipative systems. Chem Phys 2004. [DOI: 10.1016/j.chemphys.2003.10.009] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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23
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Shi Q, Geva E. A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling. J Chem Phys 2003. [DOI: 10.1063/1.1624830] [Citation(s) in RCA: 91] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
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24
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Wang H, Thoss M. Self-consistent hybrid approach for simulating electron transfer reactions in condensed phases. Isr J Chem 2002. [DOI: 10.1560/kj0g-kb9c-g0jb-area] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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Liao JL, Voth GA. A Centroid Molecular Dynamics Approach for Nonadiabatic Dynamical Processes in Condensed Phases: the Spin-Boson Case. J Phys Chem B 2002. [DOI: 10.1021/jp020978d] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Jie-Lou Liao
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, 315 S. 1400 E. Rm 2020, Salt Lake City, Utah 84112-0850
| | - Gregory A. Voth
- Department of Chemistry and Henry Eyring Center for Theoretical Chemistry, University of Utah, 315 S. 1400 E. Rm 2020, Salt Lake City, Utah 84112-0850
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27
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Jang S, Cao J, Silbey RJ. Fourth-order quantum master equation and its Markovian bath limit. J Chem Phys 2002. [DOI: 10.1063/1.1445105] [Citation(s) in RCA: 80] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
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