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Hierarchy  equations of motion approach

Quantum master equation with low temperature correction terms

bullet Y. Tanimura, Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath, Phys. Rev. A41, 6676-6687 (1990).
bulletA. Ishizaki and Y. Tanimura, Quantum dynamics of a system strongly coupled to a low temperature colored noise bath: reduced hierarchy equations approach, J. Phys. Soc. Jpn. 74, 3131 (2005). [full text PDF: OPEN SELECT]
bulletA. Ishizaki and Y. Tanimura, Modeling vibrational dephasing and energy relaxation processes of intermolecular anharmonic modes for multidimensional infrared spectroscopies, J. Chem. Phys. 125, 084501 (2006).
bulletA. Ishizaki and Y. Tanimura, Dynamics of Multimode System Coupled to Multiple Heat Baths Probed by Two-Dimensional Infrared Spectroscopy, J. Phys. Chem. A, 111, 9296 (2007).
bulletA. Ishizaki and Y. Tanimura, Nonperturbative-NonMarkovian Quantum Master Equation Approach: Validity and Limitation to Calculate Nonlinear Response Functions, Chem. Phys. 347, 185 (2008).
bulletA. G. Dijkstra and Y. Tanimura, Non-Markovian entanglement dynamics in the presence of system-bath coherence, Phys. Rev. Lett 104, 250401 (2010).
bulletA. G. Dijkstra and Y. Tanimura, Role of the Environment Time Scale on Light-Harvesting Efficiency and Coherent Oscillations, New J. Phys. 14, 073027 [11pages] (2012).[Open Access]
bulletA. G. Dijkstra and Y. Tanimura, Linear and third- and fifth-order nonlinear spectroscopy of a charge transfer system coupled to an underdamped vibration, J. Chem. Phys. 142, 212423 [7 pages] (2015).
bulletY. Tanimura, Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities, J. Chem. Phys. 141, 044114 (2014). [Open Access]
bulletM. Tsuchimoto and Y. Tanimura, Spins Dynamics in a Dissipative Environment: Hierarchal Equations of Motion Approach using a Graphics Processing Unit (GPU), J. Chem. Theory Comput.,11, 3859-3865 (2015).

Quantum master equation for Gaussian-Markovian noise bath

bulletY. Tanimura and R. Kubo, Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 101-114 (1989). pdf file (1541k) [full text PDF: OPEN SELECT] (1.2M byte large)
bulletY. Tanimura and R. Kubo, Two-time correlation functions of a system coupled to a heat bath with a Gaussian-Markoffian interaction, J. Phys. Soc. Jpn. 58, 1199-1206 (1989). pdf file (815k)
bulletY. Tanimura, T. Suzuki and R. Kubo, Second order optical process of a three-level system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 1850-1859 (1989).  pdf file (1062k)
bulletY. Tanimura and R. Kubo, Time-dependent spectrum of a two-level system coupled to a heat bath driven by pulsed laser, J. Phys. Soc. Jpn. 58, 3001-3012 (1989). pdf file (1762k)
bulletT. Joutsuka and Y. Tanimura, Detecting the Dzyaloshinskii-Moriya Interaction by Means of Pulsed EPR Spectroscopy, Chem. Phys. Lett. 457, 237 (2008)

Quantum Fokker-Planck equation for Gaussian-Markovian noise bath

bulletY. Tanimura and P. G. Wolynes, Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath, Phys. Rev. A43, 4131-4142 (1991).
bulletY. Tanimura and P. G. Wolynes, The interplay of tunneling, resonance, and dissipation in quantum barrier crossing: A numerical study, J. Chem. Phys. 96, 8485-8496 (1992).

Quantum Fokker-Planck equation with low temperature correction terms

bulletA. Sakurai and Y. Tanimura, Does hbar play a role in multidimensional spectroscopy? Reduced hierarchy equations of motion approach to molecular vibrations, J. Phys. Chem. A 115, 4009-4022 (2011) Error correction)
bulletA. Sakurai and Y. Tanimura, An approach to quantum transport based on reduced hierarchy equations of motion: Application to a resonant tunneling diode, J. Phys. Soc. Jpn 82, 033707 [4 pages] (2013).
bulletA. Sakurai and Y. Tanimura, Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira-Leggett Hamiltonian, New J. of Phys. 16, 015002 [ 24 pages] (2014). [Open Access]
bulletA. Kato and Y. Tanimura, Quantum Suppression of Ratchet Rectification in a Brownian System Driven by a Biharmonic Force, J. Phys. Chem. B 117, 13132-13144 (2013).
bulletY. Tanimura, Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations, J. Chem. Phys. 142, 144110 [20 pages] (2015) (PDF) [Open Access]

Multistate quantum Fokker-Planck equation

bulletY. Tanimura and S. Mukamel, Multistate quantum Fokker-Planck approach to nonadiabatic wave packet dynamics in pump-probe spectroscopy, J. Chem. Phys. 101, 3049-3061 (1994).
bulletY. Tanimura and Y. Maruyama, Gaussian-Markovian quantum Fokker-Planck approach to nonlinear spectroscopy of a displaced Morse potentials system: dissociation, predissociation and optical Stark effects, J. Chem. Phys. 107, 1779-1793 (1997).
bulletY. Maruyama and Y. Tanimura, Pump-probe spectra and nuclear dynamics for a dissipative molecular system in a strong laser field: predissociation dynamics, Chem. Phys. Lett. 292, 28-34 (1998).
bullet T. Ikeda and Y Tanimura, Probing photoisomerization processes by means of multi-dimensional electronic spectroscopy: The multi-state quantum hierarchal Fokker-Planck Equation approach,

Calculations of correlation functions

bulletY. Tanimura, Fifth-order two-dimensional vibrational spectroscopy of a Morse potential system in condensed phases, Chem. Phys. 233, 217-229 (1998).

Quantum Fokker-Planck equation with nonlinear system-bath coupling

bulletT. Steffen and Y. Tanimura, Two dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions: I. Gaussian-white case, J. Phys. Soc. Jpn. 69, 3115-3132 (2000).pdf file(608k) [full text PDF: OPEN SELECT] ; 76, 078001(2007).Erratum PDF
bulletY. Tanimura and T. Steffen, Two dimensional spectroscopy for harmonic vibrational modes with nonlinear system-bath interactions: II. Gaussian-Markovian case, J. Phys. Soc. Jpn. 69, 4095-4106 (2000). Pdf file(366k) [full text PDF: OPEN SELECT]
bulletT. Kato and Y. Tanimura, Vibrational spectroscopy of a harmonic oscillator system nonlinearly coupled to a heat bath, J. Chem. Phys. 117, 6221-6234(2002).
bulletT. Kato and Y. Tanimura, Two-dimensional Raman and infrared vibrational spectroscopy for a harmonic oscillator system nonlinearly coupled with a colored noise bath, J. Chem. Phys. 120, 260-271 (2004).
bulletA.Ishizaki and Y. Tanimura, Multidimensional vibrational spectroscopy for tunneling processes in a dissipative environment,   J. Chem. Phys. 123, 14503 (2005)
bulletT. Ikeda, H. Ito, and Y. Tanimura, Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions, J. Chem. Phys. 142, 212421 [15 pages] (2015).

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Quantum master equation for general noise bath

bulletY. Tanimura, Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath, Phys. Rev. A41, 6676-6687 (1990).
bulletY. Tanimura and S. Mukamel, Optical Stark spectroscopy of Brownian oscillator in intense fields, J. Phys. Soc. Jpn. 63, 66-77 (1994). [full text PDF: OPEN SELECT] (1.3M byte)
bulletY. Tanimura and S. Mukamel, Electronic Dephasing in Femtosecond Curve Crossing Spectroscopy, Proceedings of the fourteenth international conference on Raman Spectroscopy, Ed. by N.T. Yu and X.-Y. Li, 23-26 (John Wiley & Sons, 1994).pdf file (292k),
bulletA. Ishizaki and Y. Tanimura, Modeling vibrational dephasing and energy relaxation processes of intermolecular anharmonic modes for multidimensional infrared spectroscopies, J. Chem. Phys. 125, 084501 (2006).
bulletM. Tanaka and Y. Tanimura, Quantum Dissipative Dynamics of Electron Transfer Reaction System: Nonperturbative Hierarchy Equation Approach, J. Phys. Soc. Jpn, 78, 073802 (2009).
bulletM. Tanaka and Y. Tanimura, Multistate Electron Transfer Dynamics in the Condensed Phase: Exact Calculations from the Reduced Hierarchy Equations of Motion Approach, J. Chem. Phys. 132, 214502 (2010)
bulletY. Tanimura, Reduced hierarchy equations of motion approach with Drude plus Brownian spectral distribution: Probing electron transfer processes by means of two-dimensional correlation spectroscopy, J. Chem, Phys 137, 22A550 [9 pages] (2012). [Open Access]

Review article

bulletY. Tanimura, Stochastic Liouville, Langevin, Fokker-Planck, and master equation approaches to quantum dissipative systems, J. Phys. Soc. Jpn.  75,  082001  (2006).  [full text PDF: OPEN SELECT] (6M byte large)

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