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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: 140] [Impact Index Per Article: 46.7] [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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Affiliation(s)
- Hou-Dao Zhang
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Rui-Xue Xu
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao Zheng
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China
- iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), University of Science and Technology of China, Hefei, Anhui 230026, China
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Ding JJ, Wang Y, Zhang HD, Xu RX, Zheng X, Yan Y. Fokker-Planck quantum master equation for mixed quantum-semiclassical dynamics. J Chem Phys 2017; 146:024104. [PMID: 28088143 DOI: 10.1063/1.4973610] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We revisit Caldeira-Leggett's quantum master equation representing mixed quantum-classical theory, but with limited applications. Proposed is a Fokker-Planck quantum master equation theory, with a generic bi-exponential correlation function description on semiclassical Brownian oscillators' environments. The new theory has caustic terms that bridge between the quantum description on primary systems and the semiclassical or quasi-classical description on environments. Various parametrization schemes, both analytical and numerical, for the generic bi-exponential environment bath correlation functions are proposed and scrutinized. The Fokker-Planck quantum master equation theory is of the same numerical cost as the original Caldeira-Leggett's approach but acquires a significantly broadened validity and accuracy range, as illustrated against the exact dynamics on model systems in quantum Brownian oscillators' environments, at moderately low temperatures.
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Affiliation(s)
- Jin-Jin Ding
- School of Chemistry and Chemical Engineering, Nantong University, Nantong, Jiangsu 226019, China
| | - Yao Wang
- 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
| | - 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
| | - 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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Zhang HD, Qiao Q, Xu RX, Yan Y. Solvent-induced polarization dynamics and coherent two-dimensional spectroscopy: Dissipaton equation of motion approach. Chem Phys 2016. [DOI: 10.1016/j.chemphys.2016.07.005] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Zhang HD, Qiao Q, Xu RX, Yan Y. Effects of Herzberg–Teller vibronic coupling on coherent excitation energy transfer. J Chem Phys 2016; 145:204109. [DOI: 10.1063/1.4968031] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.6] [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 Synergetic Innovation Center of Quantum Information and Quantum Physics and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Qin Qiao
- Discipline of Neuroscience and Department of Anatomy, Histology and Embryology, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - Rui-Xue Xu
- Discipline of Neuroscience and Department of Anatomy, Histology and Embryology, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and Department of Chemical Physics and Synergetic Innovation Center of Quantum Information and Quantum Physics and iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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Ding JJ, Zhang HD, Wang Y, Xu RX, Zheng X, Yan Y. Minimum-exponents ansatz for molecular dynamics and quantum dissipation. J Chem Phys 2016; 145:204110. [DOI: 10.1063/1.4967964] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Jin-Jin Ding
- School of Chemistry and Chemical Engineering, Nantong University, Nantong, Jiangsu 226019, China
| | - 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
| | - Yao Wang
- 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
| | - 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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Ye L, Wang X, Hou D, Xu RX, Zheng X, Yan Y. HEOM-QUICK: a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2016. [DOI: 10.1002/wcms.1269] [Citation(s) in RCA: 70] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- LvZhou Ye
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Xiaoli Wang
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Dong Hou
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Rui-Xue Xu
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale and Synergetic Innovation Center of Quantum Information and Quantum Physics; University of Science and Technology of China; Hefei China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale and iChEM (Collaborative Innovation Center of Chemistry for Energy Materials); University of Science and Technology of China; Hefei China
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Zhang HD, Yan Y. Kinetic Rate Kernels via Hierarchical Liouville–Space Projection Operator Approach. J Phys Chem A 2016; 120:3241-5. [DOI: 10.1021/acs.jpca.5b11731] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hou-Dao Zhang
- Department
of Chemistry, Hong Kong University of Science and Technology, Hong Kong, China
| | - YiJing Yan
- Department
of Chemistry, Hong Kong University of Science and Technology, Hong Kong, China
- Hefei
National Laboratory for Physical Sciences at the Microscale, iChEM (Collaborative Innovation Center of Chemistry for
Energy Materials), University of Science and Technology of China, Hefei 230026, China
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