Path integrals Methods
 Generating functional approach to displaced harmonic oscillators systems. 
 Generating functional approach to the quantum Brownian system. 
 Study the effects of anharmonisity from preservative expansion approach. 
 Generalization of optimized perturbation theory to study the dissipative
system. 
 Calculations of correlation functions of a free rotator in a dissipative
environment. 
Representative references
 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, 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). 
 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). 
 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. 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] 
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