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Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath

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Quantum Statistical Mechanical Theory of the Rate of Exchange Chemical Reactions in the Gas Phase

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Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath

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Trajectory analysis of a kinetic theory for isomerization dynamics in condensed phases

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Relaxation processes and chemical kinetics

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Quantum Fokker-Planck equation

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A Derivation of Generalized Semi-Classical Langevin Equations Based on the Feynman Path-Integral Approach

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Theory of open quantum systems

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Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems

Tanimura, Y. (2006) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.75.082001 · Cited by 891 · see citing works

Numerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

Tanimura, Y. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0011599 · Cited by 536 · see citing works

Quantum Dynamics of System Strongly Coupled to Low-Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach

Ishizaki, A., & Tanimura, Y. (2005) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.74.3131 · Cited by 510 · see citing works

Non-Markovian evolution of the density operator in the presence of strong laser fields

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Fisher information under decoherence in Bloch representation

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Electron Transfer Rates in Bridged Molecular Systems 2. A Steady-State Analysis of Coherent Tunneling and Thermal Transitions

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Quantum rates for a double well coupled to a dissipative bath: Accurate path integral results and comparison with approximate theories

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Efficient hierarchical Liouville space propagator to quantum dissipative dynamics

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Exact quantum master equation via the calculus on path integrals

Xu, R., Cui, P., Li, X.-Q., Mo, Y., & Yan, Y. (2005) · The Journal of Chemical Physics · doi:10.1063/1.1850899 · Cited by 276 · see citing works

Hierarchical approach based on stochastic decoupling to dissipative systems

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Non-Markovian Entanglement Dynamics in the Presence of System-Bath Coherence

Dijkstra, A. G., & Tanimura, Y. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.250401 · Cited by 207 · see citing works

Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities

Tanimura, Y. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4890441 · Cited by 190 · see citing works

QUANTUM MECHANICS OF DISSIPATIVE SYSTEMS

Yan, Y., & Xu, R. (2004) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.55.091602.094425 · Cited by 189 · see citing works

Open Quantum Dynamics Calculations with the Hierarchy Equations of Motion on Parallel Computers

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Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach

Xu, R., & Yan, Y. (2007) · Physical Review E · doi:10.1103/physreve.75.031107 · Cited by 177 · see citing works

Entanglement dynamics of two qubits in a common bath

Ma, J., Sun, Z., Wang, X., & Nori, F. (2012) · Physical Review A · doi:10.1103/physreva.85.062323 · Cited by 156 · see citing works

Modified Scaled Hierarchical Equation of Motion Approach for the Study of Quantum Coherence in Photosynthetic Complexes

Zhu, J., Kais, S., Rebentrost, P., & Aspuru-Guzik, A. (2011) · The Journal of Physical Chemistry B · doi:10.1021/jp109559p · Cited by 141 · see citing works

Optical line shapes of molecular aggregates: Hierarchical equations of motion method

Chen, L., Zheng, R., Shi, Q., & Yan, Y. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3213013 · Cited by 135 · see citing works

Effective-mode representation of non-Markovian dynamics: A hierarchical approximation of the spectral density. I. Application to single surface dynamics

Hughes, K. H., Christ, C. D., & Burghardt, I. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3159671 · Cited by 134 · see citing works

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

Tanimura, Y. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4916647 · Cited by 132 · see citing works

Real-time path-integral approach to quantum coherence and dephasing in nonadiabatic transitions and nonlinear optical response

Tanimura, Y., & Mukamel, S. (1993) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.47.118 · Cited by 132 · see citing works

Non-Markovian quantum jumps in excitonic energy transfer

Rebentrost, P., Chakraborty, R., & Aspuru‐Guzik, A. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3259838 · Cited by 128 · see citing works

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy

Tanimura, Y. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4766931 · Cited by 130 · see citing works

Non-Markovian theories based on a decomposition of the spectral density

Kleinekathöfer, U. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1770619 · Cited by 126 · see citing works

An open quantum systems approach to proton tunnelling in DNA

Slocombe, L., Sacchi, M., & Al-Khalili, J. (2022) · Communications Physics · doi:10.1038/s42005-022-00881-8 · Cited by 122 · see citing works

HEOM‐QUICK : a program for accurate, efficient, and universal characterization of strongly correlated quantum impurity systems

Ye, L., Wang, X., Hou, D., Xu, R., Zheng, X. H., & Yan, Y. (2016) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1269 · Cited by 120 · see citing works

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Ishizaki, A., & Tanimura, Y. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2244558 · Cited by 115 · see citing works

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

Kelly, A., & Markland, T. E. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4812355 · Cited by 116 · see citing works

Why Quantum Coherence Is Not Important in the Fenna–Matthews–Olsen Complex

Wilkins, D. M., & Dattani, N. S. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/ct501066k · Cited by 113 · see citing works

The interplay of tunneling, resonance, and dissipation in quantum barrier crossing: A numerical study

Tanimura, Y., & Wolynes, P. G. (1992) · The Journal of Chemical Physics · doi:10.1063/1.462301 · Cited by 114 · see citing works

Quantum Dissipative Dynamics of Electron Transfer Reaction System: Nonperturbative Hierarchy Equations Approach

Tanaka, M., & Tanimura, Y. (2009) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.78.073802 · Cited by 112 · see citing works

Nonperturbative non-Markovian quantum master equation: Validity and limitation to calculate nonlinear response functions

Ishizaki, A., & Tanimura, Y. (2007) · Chemical Physics · doi:10.1016/j.chemphys.2007.10.037 · Cited by 112 · see citing works

Quantum speed limits in open systems: Non-Markovian dynamics without rotating-wave approximation

Sun, Z., Liu, J., Ma, J., & Wang, X. (2015) · Scientific Reports · doi:10.1038/srep08444 · Cited by 107 · see citing works

Multistate quantum Fokker–Planck approach to nonadiabatic wave packet dynamics in pump–probe spectroscopy

Tanimura, Y., & Mukamel, S. (1994) · The Journal of Chemical Physics · doi:10.1063/1.467618 · Cited by 104 · see citing works

Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy

Tanimura, Y. (2012) · Desy publication database (The Deutsches Elektronen-Synchrotron) · Cited by 103 · see citing works

Multistate electron transfer dynamics in the condensed phase: Exact calculations from the reduced hierarchy equations of motion approach

Tanaka, M., & Tanimura, Y. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3428674 · Cited by 101 · see citing works

Electron transfer dynamics: Zusman equation versus exact theory

Shi, Q., Chen, L., Nan, G., Xu, R., & Yan, Y. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3125003 · Cited by 100 · see citing works

Modified Scaled Hierarchical Equation of Motion Approach for the Study of Quantum Coherence in Photosynthetic Complexes

Zhu, J., Kais, S., Rebentrost, P., & Aspuru‐Guzik, A. (2011) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 98 · see citing works

Modeling, Calculating, and Analyzing Multidimensional Vibrational Spectroscopies

Tanimura, Y., & Ishizaki, A. (2009) · Accounts of Chemical Research · doi:10.1021/ar9000444 · Cited by 94 · see citing works

Non-Markovian Quantum Jumps in Excitonic Energy Transfer

Rebentrost, P., Chakraborty, R., & Aspuru‐Guzik, A. (2009) · Digital Access to Scholarship at Harvard (DASH) (Harvard University) · Cited by 93 · see citing works

Dynamics of a Multimode System Coupled to Multiple Heat Baths Probed by Two-Dimensional Infrared Spectroscopy

Ishizaki, A., & Tanimura, Y. (2007) · The Journal of Physical Chemistry A · doi:10.1021/jp072880a · Cited by 88 · see citing works

Optical Stark Spectroscopy of a Brownian Oscillator in Intense Fields

Tanimura, Y., & Mukamel, S. (1994) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.63.66 · Cited by 91 · see citing works

Quantum Fokker-Planck theory in a non-Gaussian-Markovian medium

Yan, Y. (1998) · Physical Review A · doi:10.1103/physreva.58.2721 · Cited by 90 · see citing works

Dissipation equation of motion approach to open quantum systems

Yan, Y., Jin, J., Xu, R., & Zheng, X. H. (2016) · Frontiers of Physics · doi:10.1007/s11467-016-0513-5 · Cited by 87 · see citing works

A phase-space study of Bloch–Redfield theory

Cao, J. (1997) · The Journal of Chemical Physics · doi:10.1063/1.474670 · Cited by 86 · see citing works

Dynamics of a One-Dimensional Holstein Polaron with the Hierarchical Equations of Motion Approach

Chen, L., Zhao, Y., & Tanimura, Y. (2015) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.5b01368 · Cited by 81 · see citing works

Ultrafast Nonadiabatic Dynamics of Singlet Fission: Quantum Dynamics with the Multilayer Multiconfigurational Time-Dependent Hartree (ML-MCTDH) Method

Zheng, J., Xie, Y. Y., Jiang, S., & Lan, Z. (2016) · The Journal of Physical Chemistry C · doi:10.1021/acs.jpcc.5b09921 · Cited by 81 · see citing works

Removing instabilities in the hierarchical equations of motion: Exact and approximate projection approaches

Dunn, I. S., Tempelaar, R., & Reichman, D. R. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5092616 · Cited by 75 · see citing works

Does ℏ Play a Role in Multidimensional Spectroscopy? Reduced Hierarchy Equations of Motion Approach to Molecular Vibrations

Sakurai, A., & Tanimura, Y. (2011) · The Journal of Physical Chemistry A · doi:10.1021/jp1095618 · Cited by 75 · see citing works

Gaussian–Markovian quantum Fokker–Planck approach to nonlinear spectroscopy of a displaced Morse potentials system: Dissociation, predissociation, and optical Stark effects

Tanimura, Y., & Maruyama, Y. (1997) · The Journal of Chemical Physics · doi:10.1063/1.474531 · Cited by 75 · see citing works

Two-Dimensional Spectroscopy for Harmonic Vibrational Modes with Nonlinear System-Bath Interactions. II. Gaussian-Markovian Case

Tanimura, Y., & Steffen, T. (2000) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.69.4095 · Cited by 75 · see citing works

Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath

Kato, T., & Tanimura, Y. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1629272 · Cited by 74 · see citing works

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

Jin, J., Welack, S., Luo, J., Li, X.-Q., Cui, P., Xu, R., & Yan, Y. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2713104 · Cited by 72 · see citing works

Quantum heat transport of a two-qubit system: Interplay between system-bath coherence and qubit-qubit coherence

Kato, A., & Tanimura, Y. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4928192 · Cited by 68 · see citing works

Hierarchical equations of motion method based on Fano spectrum decomposition for low temperature environments

Zhang, H.-D., Cui, L., Gong, H., Xu, R., Zheng, X. H., & Yan, Y. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5136093 · Cited by 66 · see citing works

Reduced dynamics of coupled harmonic and anharmonic oscillators using higher-order perturbation theory

Schröder, M., Schreiber, M., & Kleinekathöfer, U. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2538754 · Cited by 66 · see citing works

Hierarchical quantum master equation approach to electronic-vibrational coupling in nonequilibrium transport through nanosystems: Reservoir formulation and application to vibrational instabilities

Schinabeck, C., Härtle, R., & Thoss, M. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.235429 · Cited by 63 · see citing works

Optimal control of quantum non-Markovian dissipation: Reduced Liouville-space theory

Xu, R., Yan, Y., Ohtsuki, Y., Fujimura, Y., & RABITZ, H. A. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1665486 · Cited by 63 · see citing works

Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath

Kato, T., & Tanimura, Y. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1503778 · Cited by 62 · see citing works

Non-equilibrium dynamics from RPMD and CMD

Welsch, R., Song, K., Shi, Q., Althorpe, S. C., & Miller, T. F. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4967958 · Cited by 62 · see citing works

Wigner function approach to the quantum Brownian motion of a particle in a potential

Coffey, W. T., Kalmykov, Y. P., Титов, С. В., & Mulligan, B. P. (2007) · Physical Chemistry Chemical Physics · doi:10.1039/b614554j · Cited by 59 · see citing works

Fifth-order two-dimensional vibrational spectroscopy of a Morse potential system in condensed phases

Tanimura, Y. (1998) · Chemical Physics · doi:10.1016/s0301-0104(98)00010-x · Cited by 59 · see citing works

Two-Dimensional Spectroscopy for Harmonic Vibrational Modes with Nonlinear System-Bath Interactions. I. Gaussian-White Case

Steffen, T., & Tanimura, Y. (2000) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.69.3115 · Cited by 55 · see citing works

Approach to quantum Kramers’ equation and barrier crossing dynamics

Banerjee, D., Bag, B. C., Banik, S. K., & Ray, D. S. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.021109 · Cited by 55 · see citing works

Dissipative dynamics at conical intersections: simulations with the hierarchy equations of motion method

Chen, L., Gelin, M. F., Chernyak, V., Domcke, W., & Zhao, Y. (2016) · Faraday Discussions · doi:10.1039/c6fd00088f · Cited by 53 · see citing works

Unified approach to the Bloch–Redfield theory and quantum Fokker–Planck equations

Yan, Y., Shuang, F., Xu, R., Cheng, J., Li, X.-Q., Chen, Y., & Zhang, H. (2000) · The Journal of Chemical Physics · doi:10.1063/1.482018 · Cited by 53 · see citing works

Quantum rate dynamics for proton transfer reactions in condensed phase: The exact hierarchical equations of motion approach

Chen, L., & Shi, Q. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3097128 · Cited by 52 · see citing works

Spin squeezing under non-Markovian channels by the hierarchy equation method

Yin, X., Ma, J., Wang, X., & Nori, F. (2012) · Physical Review A · doi:10.1103/physreva.86.012308 · Cited by 51 · see citing works

The Caldeira–Leggett quantum master equation in Wigner phase space: continued-fraction solution and application to Brownian motion in periodic potentials

García-Palacios, J. L., & Zueco, D. (2004) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/37/45/003 · Cited by 51 · see citing works

Current-induced bond rupture in single-molecule junctions

Erpenbeck, A., Schinabeck, C., Peskin, U., & Thoss, M. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.235452 · Cited by 50 · see citing works

Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions

Ikeda, T., Ito, H., & Tanimura, Y. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4917033 · Cited by 49 · see citing works

Open Systems with Error Bounds: Spin-Boson Model with Spectral Density Variations

Mascherpa, F., Smirne, A., Huelga, S. F., & Plenio, M. B. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.100401 · Cited by 51 · see citing works

Semiclassical Klein–Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

Coffey, W. T., Kalmykov, Y. P., Титов, С. В., & Mulligan, B. P. (2006) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/3/f02 · Cited by 49 · see citing works

Simulating two-dimensional infrared-Raman and Raman spectroscopies for intermolecular and intramolecular modes of liquid water

Ito, H., & Tanimura, Y. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4941842 · Cited by 48 · see citing works

Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures

Erpenbeck, A., Hertlein, C., Schinabeck, C., & Thoss, M. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5041716 · Cited by 46 · see citing works

Exact dynamics of quantum correlations of two qubits coupled to bosonic baths

Wang, C., & Chen, Q.-H. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/10/103020 · Cited by 48 · see citing works

Smoluchowski equation approach for quantum Brownian motion in a tilted periodic potential

Coffey, W. T., Kalmykov, Y. P., Титов, С. В., & Cleary, L. (2008) · Physical Review E · doi:10.1103/physreve.78.031114 · Cited by 45 · see citing works

Multidimensional vibrational spectroscopy for tunneling processes in a dissipative environment

Ishizaki, A., & Tanimura, Y. (2005) · The Journal of Chemical Physics · doi:10.1063/1.1906215 · Cited by 43 · see citing works

Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force

Kato, A., & Tanimura, Y. (2013) · The Journal of Physical Chemistry B · doi:10.1021/jp403056h · Cited by 40 · see citing works

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions

Banik, S. K., Bag, B. C., & Ray, D. S. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.051106 · Cited by 40 · see citing works

Chebyshev hierarchical equations of motion for systems with arbitrary spectral densities and temperatures

Rahman, H., & Kleinekathöfer, U. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5100102 · Cited by 39 · see citing works

A new method to account for the difference between classical and quantum baths in quantum dissipative dynamics

Zhu, L., Liu, H., & Shi, Q. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/9/095020 · Cited by 38 · see citing works

On the exact truncation tier of fermionic hierarchical equations of motion

Han, L., Zhang, H.-D., Zheng, X. H., & Yan, Y. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5034776 · Cited by 37 · see citing works

Unified time-path approach to the effect of anharmonicity on the molecular vibrational spectroscopy in solution

Okumura, K., & Tanimura, Y. (1996) · The Journal of Chemical Physics · doi:10.1063/1.472589 · Cited by 36 · see citing works

Finite-time Landau-Zener processes and counterdiabatic driving in open systems: Beyond Born, Markov, and rotating-wave approximations

Sun, Z., Zhou, L., Xiao, G., Poletti, D., & Gong, J. (2016) · Physical Review A · doi:10.1103/physreva.93.012121 · Cited by 35 · see citing works

Quantum dynamics for dissipative systems: A numerical study of the Wigner–Fokker–Planck equation

Zhang, S., & Pollak, E. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1543139 · Cited by 35 · see citing works

Probing photoisomerization processes by means of multi-dimensional electronic spectroscopy: The multi-state quantum hierarchical Fokker-Planck equation approach

Ikeda, T., & Tanimura, Y. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4989537 · Cited by 34 · see citing works

Lead geometry and transport statistics in molecular junctions

Ridley, M., Gull, E., & Cohen, G. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5096244 · Cited by 34 · see citing works

Capturing non-Markovian dynamics with the reaction coordinate method

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Stochastically averaged master equation for a quantum-dynamic system interacting with a thermal bath

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