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Bi RH, Su Y, Wang Y, Sun L, Dou W. Spin-lattice relaxation with non-linear couplings: Comparison between Fermi's golden rule and extended dissipaton equation of motion. J Chem Phys 2024; 161:024105. [PMID: 38984964 DOI: 10.1063/5.0212870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/07/2024] [Accepted: 06/24/2024] [Indexed: 07/11/2024] Open
Abstract
Fermi's golden rule (FGR) offers an empirical framework for understanding the dynamics of spin-lattice relaxation in magnetic molecules, encompassing mechanisms like direct (one-phonon) and Raman (two-phonon) processes. These principles effectively model experimental longitudinal relaxation rates, denoted as T1-1. However, under scenarios of increased coupling strength and nonlinear spin-lattice interactions, FGR's applicability may diminish. This paper numerically evaluates the exact spin-lattice relaxation rate kernels, employing the extended dissipaton equation of motion formalism. Our calculations reveal that when quadratic spin-lattice coupling is considered, the rate kernels exhibit a free induction decay-like feature, and the damping rates depend on the interaction strength. We observe that the temperature dependence predicted by FGR significantly deviates from the exact results since FGR ignores the higher order effects and the non-Markovian nature of spin-lattice relaxation. Our methods can be easily extended to study other systems with nonlinear spin-lattice interactions and provide valuable insights into the temperature dependence of T1 in molecular qubits when the coupling is strong.
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Affiliation(s)
- Rui-Hao Bi
- Department of Chemistry, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310024, China
| | - Yu Su
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Hefei National Research Center for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lei Sun
- Department of Chemistry, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310024, China
| | - Wenjie Dou
- Department of Chemistry, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310024, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou, Zhejiang 310024, China
- Key Laboratory for Quantum Materials of Zhejiang Province, Department of Physics, School of Science and Research Center for Industries of the Future, Westlake University, Hangzhou, Zhejiang 310024, China
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2
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Liu W, Chen ZH, Su Y, Wang Y, Dou W. Predicting rate kernels via dynamic mode decomposition. J Chem Phys 2023; 159:144110. [PMID: 37823462 DOI: 10.1063/5.0170512] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2023] [Accepted: 09/25/2023] [Indexed: 10/13/2023] Open
Abstract
Simulating dynamics of open quantum systems is sometimes a significant challenge, despite the availability of various exact or approximate methods. Particularly when dealing with complex systems, the huge computational cost will largely limit the applicability of these methods. In this work, we investigate the usage of dynamic mode decomposition (DMD) to evaluate the rate kernels in quantum rate processes. DMD is a data-driven model reduction technique that characterizes the rate kernels using snapshots collected from a small time window, allowing us to predict the long-term behaviors with only a limited number of samples. Our investigations show that whether the external field is involved or not, the DMD can give accurate prediction of the result compared with the traditional propagations, and simultaneously reduce the required computational cost.
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Affiliation(s)
- Wei Liu
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024 Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024 Zhejiang, China
| | - Zi-Hao Chen
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yu Su
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Wenjie Dou
- Department of Chemistry, School of Science, Westlake University, Hangzhou 310024 Zhejiang, China
- Institute of Natural Sciences, Westlake Institute for Advanced Study, Hangzhou 310024 Zhejiang, China
- Department of Physics, School of Science, Westlake University, Hangzhou 310024, Zhejiang, China
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Su Y, Chen ZH, Zhu H, Wang Y, Han L, Xu RX, Yan Y. Electron Transfer under the Floquet Modulation in Donor-Bridge-Acceptor Systems. J Phys Chem A 2022; 126:4554-4561. [PMID: 35786902 DOI: 10.1021/acs.jpca.2c03308] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Electron transfer (ET) processes are of broad interest in modern chemistry. With the advancements of experimental techniques, one may modulate the ET via such events as light-matter interactions. In this work, we study the ET under a Floquet modulation occurring in the donor-bridge-acceptor systems, with the rate kernels projected out from the exact dissipaton equation of motion formalism. This together with the Floquet theorem enables us to investigate the interplay between the intrinsic non-Markovianity and the driving periodicity. The observed rate kernel exhibits a Herzberg-Teller-like mechanism induced by the bridge fluctuation subject to effective modulation.
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Affiliation(s)
- Yu Su
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zi-Hao Chen
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Haojie Zhu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Yao Wang
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Lu Han
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Department of Chemical Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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Tanimura Y. Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM). J Chem Phys 2021; 153:020901. [PMID: 32668942 DOI: 10.1063/5.0011599] [Citation(s) in RCA: 163] [Impact Index Per Article: 54.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.
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Affiliation(s)
- Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Seibt J, Kühn O. Exciton transfer using rates extracted from the “hierarchical equations of motion”. J Chem Phys 2020; 153:194112. [DOI: 10.1063/5.0027373] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Joachim Seibt
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
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Yan Y, Xu M, Liu Y, Shi Q. Theoretical study of charge carrier transport in organic molecular crystals using the Nakajima-Zwanzig-Mori generalized master equation. J Chem Phys 2019; 150:234101. [DOI: 10.1063/1.5096214] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023] Open
Affiliation(s)
- 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
| | - Yanying Liu
- 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, 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; University of Chinese Academy of Sciences, Beijing 100049, China; and Physical Science Laboratory, Huairou National Comprehensive Science Center, Beijing 101407, China
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9
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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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Zhang HD, Qiao Q, Xu RX, Zheng X, Yan Y. Efficient steady-state solver for hierarchical quantum master equations. J Chem Phys 2017; 147:044105. [DOI: 10.1063/1.4995424] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Hou-Dao Zhang
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qin Qiao
- Discipline of Neuroscience, Department of Anatomy, Histology and Embryology, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and iChEM and Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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11
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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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12
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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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