Hierarchy equations of motion approach
Quantum master equation with low temperature correction terms

Y. Tanimura, Nonperturbative expansion method for a
quantum system coupled to a harmonicoscillator bath,
Phys.
Rev. A41, 66766687 (1990).

 A. 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]

 A. 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). 
 A. Ishizaki and Y. Tanimura, Dynamics of Multimode System
Coupled to Multiple Heat Baths Probed by TwoDimensional Infrared
Spectroscopy,
J. Phys. Chem. A,
111, 9296 (2007). 
 A. Ishizaki and Y. Tanimura, NonperturbativeNonMarkovian Quantum
Master Equation Approach:
Validity and Limitation to Calculate Nonlinear Response Functions,
Chem. Phys.
347, 185 (2008).

 A. G. Dijkstra and Y. Tanimura, NonMarkovian
entanglement dynamics in the presence of systembath coherence,
Phys. Rev. Lett
104, 250401 (2010). 
 A. G. Dijkstra and Y. Tanimura, Role of the
Environment Time Scale on LightHarvesting Efficiency and Coherent
Oscillations,
New J. Phys.
14, 073027
[11pages] (2012).[Open Access] 
 A. G. Dijkstra and Y. Tanimura, Linear and
third and fifthorder nonlinear spectroscopy of a charge transfer
system coupled to an underdamped vibration,
J. Chem. Phys. 142, 212423 [7 pages] (2015).

 Y. 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] 
 M. 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,
38593865 (2015). 
Quantum master equation for GaussianMarkovian noise
bath
 Y. Tanimura and R. Kubo, Time evolution of a quantum
system in contact with a nearly GaussianMarkoffian noise bath, J.
Phys. Soc. Jpn. 58, 101114 (1989).
pdf
file (1541k)
[full
text PDF: OPEN SELECT]
(1.2M byte large) 
 Y. Tanimura and R. Kubo, Twotime correlation functions
of a system coupled to a heat bath with a GaussianMarkoffian interaction,
J. Phys. Soc. Jpn. 58, 11991206 (1989).
pdf
file (815k) 
 Y. Tanimura, T. Suzuki and R. Kubo, Second order optical
process of a threelevel system in contact with a nearly GaussianMarkoffian
noise bath, J. Phys. Soc. Jpn. 58, 18501859 (1989).
pdf
file (1062k) 
 Y. Tanimura and R. Kubo, Timedependent spectrum of a
twolevel system coupled to a heat bath driven by pulsed laser,
J. Phys.
Soc. Jpn. 58, 30013012 (1989).
pdf file
(1762k) 
 T. Joutsuka and Y. Tanimura,
Detecting the DzyaloshinskiiMoriya Interaction by Means
of Pulsed EPR Spectroscopy,
Chem. Phys. Lett.
457, 237 (2008) 
Quantum FokkerPlanck equation for GaussianMarkovian
noise bath
Quantum FokkerPlanck equation with low temperature correction terms
 A. 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, 40094022 (2011)
Error correction)

 A. 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). 
 A. Sakurai and Y. Tanimura, Selfexcited current
oscillations in a resonant tunneling diode described by a model based on
the CaldeiraLeggett Hamiltonian,
New J. of Phys.
16, 015002 [ 24 pages] (2014). [Open Access] 
 A. Kato and Y. Tanimura, Quantum Suppression of
Ratchet Rectification in a Brownian System Driven by a Biharmonic Force,
J. Phys. Chem. B
117, 1313213144 (2013). 
 Y. Tanimura, RealTime and ImaginaryTime Quantum Hierarchal FokkerPlanck Equations,
J. Chem. Phys.
142, 144110 [20 pages] (2015)
(PDF)
[Open Access] 
Multistate quantum FokkerPlanck equation
 Y. Tanimura and S. Mukamel, Multistate quantum
FokkerPlanck approach to nonadiabatic wave packet dynamics in pumpprobe
spectroscopy, J. Chem. Phys. 101, 30493061 (1994). 
 Y. Tanimura and Y. Maruyama, GaussianMarkovian quantum
FokkerPlanck approach to nonlinear spectroscopy of a displaced Morse
potentials system: dissociation, predissociation and optical Stark effects,
J. Chem. Phys. 107,
17791793 (1997). 
 Y. Maruyama and Y. Tanimura, Pumpprobe spectra and
nuclear dynamics for a dissipative molecular system in a strong laser field:
predissociation dynamics,
Chem. Phys. Lett. 292,
2834 (1998). 

T. Ikeda and Y Tanimura, Probing photoisomerization
processes by means of multidimensional electronic spectroscopy: The
multistate quantum hierarchal FokkerPlanck Equation approach,

Calculations of correlation functions
Quantum FokkerPlanck equation with nonlinear
systembath coupling
 T. Steffen and Y. Tanimura, Two dimensional
spectroscopy for harmonic vibrational modes with nonlinear systembath
interactions: I. Gaussianwhite case, J. Phys. Soc. Jpn. 69,
31153132 (2000).pdf file(608k)
[full
text PDF: OPEN SELECT]
; 76, 078001(2007).Erratum PDF

 Y. Tanimura and T. Steffen, Two dimensional
spectroscopy for harmonic vibrational modes with nonlinear systembath
interactions: II. GaussianMarkovian case, J. Phys. Soc. Jpn.
69, 40954106 (2000). Pdf file(366k)
[full
text PDF: OPEN SELECT]

 T. Kato and Y. Tanimura, Vibrational spectroscopy of a harmonic oscillator system
nonlinearly coupled to a heat bath,
J. Chem. Phys. 117,
62216234(2002). 
 T. Kato and Y. Tanimura, Twodimensional Raman and infrared vibrational
spectroscopy for a harmonic oscillator system nonlinearly coupled with a
colored noise bath,
J. Chem. Phys.
120, 260271 (2004). 
 A.Ishizaki and Y. Tanimura, Multidimensional vibrational spectroscopy
for tunneling processes in a dissipative environment,
J. Chem. Phys.
123, 14503 (2005) 
 T. Ikeda, H. Ito, and Y. Tanimura, Analysis of 2D THzRaman spectroscopy using a nonMarkovian Brownian oscillator
model with nonlinear systembath interactions,
J. Chem. Phys. 142,
212421 [15 pages] (2015). 

T. Ikeda and Y Tanimura, Probing photoisomerization
processes by means of multidimensional electronic spectroscopy: The
multistate quantum hierarchal FokkerPlanck Equation approach,
J. Chem. Phys. 146,
014102 [10 pages] (2017) 
Quantum master equation for general noise bath
 Y. Tanimura, Nonperturbative expansion method for a
quantum system coupled to a harmonicoscillator bath,
Phys. Rev. A41,
66766687 (1990).

 Y. Tanimura and S. Mukamel, Optical Stark
spectroscopy of Brownian oscillator in intense fields, J. Phys. Soc. Jpn. 63,
6677 (1994). [full
text PDF: OPEN SELECT]
(1.3M byte) 
 Y. 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, 2326 (John Wiley & Sons, 1994).pdf file
(292k), 
 A. 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). 
 M. Tanaka and Y. Tanimura, Quantum Dissipative Dynamics
of Electron Transfer Reaction System: Nonperturbative Hierarchy Equation
Approach,
J. Phys. Soc. Jpn, 78, 073802 (2009). 
 M. 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) 
 Y. Tanimura,
Reduced hierarchy equations of motion approach with Drude plus Brownian
spectral distribution: Probing electron transfer processes by means of
twodimensional correlation spectroscopy,
J. Chem, Phys
137, 22A550 [9 pages] (2012).
[Open Access] 
Review article
 Y. Tanimura, Stochastic Liouville, Langevin, FokkerPlanck, and
master equation approaches to quantum dissipative systems,
J. Phys. Soc. Jpn.
75, 082001 (2006). [full
text PDF: OPEN SELECT]
(6M byte large) 
