Path integral methods 

Generating functional and perturbative expansions approach in Brownian models

bullet Y. Tanimura and S. Mukamel, Two-dimensional femtosecond vibrational spectroscopy of liquids, J. Chem. Phys. 99, 9496-9511 (1993).
bullet K. Okumura and Y. Tanimura, Unified time-path approach to the generating functional of Brownian oscillator system - the bilinearly corrected Feynman rule for nonequilibrium processes, Phys. Rev. E 53, 214-227 (1996).
bullet K. Okumura and Y. Tanimura, The (2n+1)th-order off-resonant spectroscopy from the (n+1)th-order anharmonicites for molecular vibrational modes in the condensed phase, J. Chem. Phys.106,1687-1698 (1997).
bullet K. Okumura and Y. Tanimura, Femtosecond two-dimensional spectroscopy from anharmonic vibrational modes of molecules in the condensed phase, J. Chem. Phys. 107, 2267-2283 (1997).
bullet K. Okumura and Y. Tanimura, Interplay of Inhomogeneity and Anharmonicity in 2D Raman Spectroscopy of Liquids, Chem. Phys. Lett., 277, 159-166. (1997).
bullet K. Okumura and Y. Tanimura, Sensitivity of two-dimensional fifth-order Raman response to the mechanism of vibrational mode-mode coupling in liquid molecules, Chem. Phys. Lett. 278, 175-183 (1997).
bullet M. Cho, K. Okumura, and Y. Tanimura, Coherent two-dimensional Raman scattering: Frequency-domain Measurement of the intra- and intermolecular vibrational interactions, J Chem. Phys. 108, 1326-1334 (1998).
bullet K. Okumura and Y. Tanimura, Two-dimensional THz spectroscopy of liquids: nonlinear vibrational response to a series of THz laser pulses, Chem. Phys. Lett. 295, 298-304 (1998).
bullet K. Okumura, A. Tokmakoff, and Y. Tanimura, Structural information from two-dimensional fifth-order Raman spectroscopy, J. Chem. Phys. 111, 492-503(1999).
bullet Y. Suzuki and Y. Tanimura, Nonequilibrium initial conditions of a Brownian oscillator system observed by two-dimensional spectroscopy, J. Chem. Phys, 115, 2267-2281 (2001).
bullet Y. Suzuki and Y. Tanimura, Probing a colored-noise induced peak of a strongly damped Brownian system by one- and two-dimensional spectroscopy, Chem. Phys. Lett., 358, 51-56 (2002).
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]
bullet Y. Tanimura, Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations, J. Chem. Phys. 142, 144110 [20 pages] (2015) (PDF) [Open Access]

Generating functional in displaced Brownian oscillators models

bulletY. Tanimura and S. Mukamel, Real-time path-integral approach to quantum coherence and dephasing in nonadiabatic transitions and nonlinear optical response, Phys. Rev. E47, 118-136 (1993).
bulletY. Tanimura and S. Mukamel, Temperature Dependence and non-Condon effects in pump-probe spectroscopy in the condensed phase, J. Opt. Soc. Am. B10, 2263-2268 (1993).
bulletY. Tanimura and S. Mukamel, Description of nonlinear optical response using phase space wavepackets, J. Phys. Chem. 97, 12596-12601 (1993). pdf file (819k).
bulletY. Tanimura and S. Mukamel, Femtosecond pump-probe spectroscopy of intermolecular vibrations in molecular dimers, J. Chem. Phys. (communications) 103, 1981-1985 (1995).
bulletY. Tanimura and K. Okumura, First-, third-, and fifth-order resonant spectroscopy of anharmonic displaced oscillators system in the condensed phase, J. Chem. Phys.106, 2078-2095 (1997).

Frequency modulation models

bulletK. Okumura and Y. Tanimura, Two-time correlation functions of a harmonic system nonbilinearly coupled to a heat bath: the spontaneous Raman spectroscopy, Phys. Rev. E. 56, 2747-2750 (1997).

Optimized perturbation approach

bulletY. Suzuki and Y. Tanimura, Optimized perturbation approach with Legendre transformation to a dissipative system: correlation functions of a Morse oscillator, Phys. Rev. E, 59, 1475-1488 (1999).

Damped quantum rotator

bulletY. Suzuki and Y. Tanimura, Quantum theory of a two-dimensional rotator in a dissipative environment: Application to Far-infrared spectroscopy, J. Phys. Soc. Jpn, 70, 1167-1170 (2001).
bulletY. Suzuki and Y. Tanimura, Two-time correlation function of a two-dimensional quantal rotator in a colored noise, J. Phys. Soc. Jpn, 71, 2414-2426 (2002).
bulletY. Suzuki and Y. Tanimura, Two-dimensional spectroscopy for two-dimensional rotator coupled to a Gaussian-Markovian noise bath,  J. Chem. Phys. 119, 1650-1660 (2003).

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