Path integral methods
Generating functional and perturbative expansions
approach in Brownian models

Y. Tanimura and S. Mukamel, Twodimensional femtosecond
vibrational spectroscopy of liquids,
J. Chem. Phys. 99, 94969511
(1993). 

K. Okumura and Y. Tanimura, Unified timepath approach
to the generating functional of Brownian oscillator system  the bilinearly
corrected Feynman rule for nonequilibrium processes,
Phys. Rev. E 53,
214227 (1996). 

K. Okumura and Y. Tanimura, The (2n+1)thorder
offresonant spectroscopy from the (n+1)thorder anharmonicites for
molecular vibrational modes in the condensed phase,
J. Chem. Phys.106,16871698 (1997). 

K. Okumura and Y. Tanimura, Femtosecond twodimensional
spectroscopy from anharmonic vibrational modes of molecules in the condensed
phase, J. Chem. Phys. 107, 22672283 (1997). 

K. Okumura and Y. Tanimura, Interplay of Inhomogeneity
and Anharmonicity in 2D Raman Spectroscopy of Liquids,
Chem. Phys. Lett.,
277, 159166. (1997). 

K. Okumura and Y. Tanimura, Sensitivity of
twodimensional fifthorder Raman response to the mechanism of vibrational
modemode coupling in liquid molecules,
Chem. Phys. Lett. 278,
175183 (1997). 

M. Cho, K. Okumura, and Y. Tanimura, Coherent
twodimensional Raman scattering: Frequencydomain Measurement of the intra
and intermolecular vibrational interactions,
J Chem. Phys. 108,
13261334 (1998). 

K. Okumura and Y. Tanimura, Twodimensional THz
spectroscopy of liquids: nonlinear vibrational response to a series of THz
laser pulses, Chem. Phys. Lett. 295, 298304 (1998). 

K. Okumura, A. Tokmakoff, and Y. Tanimura, Structural
information from twodimensional fifthorder Raman spectroscopy,
J.
Chem. Phys. 111, 492503(1999). 

Y. Suzuki and Y. Tanimura, Nonequilibrium initial conditions of a Brownian oscillator system
observed by twodimensional spectroscopy,
J. Chem. Phys, 115,
22672281 (2001). 

Y. Suzuki and Y. Tanimura, Probing a colorednoise induced peak of a
strongly damped Brownian system by one and twodimensional spectroscopy,
Chem. Phys. Lett.,
358, 5156 (2002). 
 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] 

Y. Tanimura, RealTime and ImaginaryTime Quantum Hierarchal FokkerPlanck Equations,
J. Chem. Phys.
142, 144110 [20 pages] (2015)
(PDF)
[Open Access] 
Generating functional in displaced Brownian oscillators
models
 Y. Tanimura and S. Mukamel, Realtime pathintegral
approach to quantum coherence and dephasing in nonadiabatic transitions and
nonlinear optical response,
Phys. Rev. E47, 118136 (1993). 
 Y. Tanimura and S. Mukamel, Temperature Dependence and
nonCondon effects in pumpprobe spectroscopy in the condensed phase,
J.
Opt. Soc. Am. B10, 22632268 (1993). 
 Y. Tanimura and S. Mukamel, Description of nonlinear
optical response using phase space wavepackets, J. Phys. Chem. 97,
1259612601 (1993). pdf file (819k).

 Y. Tanimura and S. Mukamel, Femtosecond pumpprobe
spectroscopy of intermolecular vibrations in molecular dimers,
J. Chem.
Phys. (communications) 103, 19811985 (1995). 
 Y. Tanimura and K. Okumura, First, third, and
fifthorder resonant spectroscopy of anharmonic displaced oscillators system
in the condensed phase,
J. Chem. Phys.106, 20782095 (1997). 
Frequency modulation models
 K. Okumura and Y. Tanimura, Twotime correlation
functions of a harmonic system nonbilinearly coupled to a heat bath: the
spontaneous Raman spectroscopy,
Phys. Rev. E. 56, 27472750
(1997). 
Optimized perturbation approach
 Y. Suzuki and Y. Tanimura, Optimized perturbation
approach with Legendre transformation to a dissipative system: correlation
functions of a Morse oscillator,
Phys. Rev. E, 59,
14751488 (1999). 
Damped quantum rotator
 Y. Suzuki and Y. Tanimura, Quantum theory of
a twodimensional rotator in a dissipative environment: Application to
Farinfrared spectroscopy,
J. Phys. Soc. Jpn, 70, 11671170 (2001). 
 Y. Suzuki and Y. Tanimura, Twotime correlation function of a twodimensional quantal rotator in a colored noise,
J. Phys. Soc. Jpn,
71, 24142426 (2002). 
 Y. Suzuki and Y. Tanimura, Twodimensional spectroscopy for
twodimensional rotator coupled to a GaussianMarkovian noise bath,
J. Chem. Phys.
119, 16501660 (2003). 
