Stochastic theory
 Studies of second order optical processes of multistate system by
stochastic theory 
 Derive the GaussianMarkovian quantum master equation to generalize the
stochastic Liouville equation. 
 Fractal noise 
 NonGaussian processes 
Representative references
 Y. Tanimura, H. Takano, and R. Kubo, Second order
optical processes of a randomly modulated multilevel atom,
J. Phys.
Soc. Jpn. 55, 45504565 (1986). 
 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).
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file (1541k)
[full
text PDF: OPEN SELECT]

 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). 
 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] 

G. Gangopadhyay, S. Ghoshal, and Yoshitaka Tanimura, A
thermal bath induced new resonance in linear and nonlinear spectra of
twolevel systems,
Chem. Phys. 242,
367385 (1999).


D. Packwood and Y. Tanimura, NonGaussian stochastic
dynamics of spins and oscillators,
Phys. Rev. E 84, 061111 [9pages] (2011) 

D. Packwood and Y. Tanimura, Dephasing by a
continuoustime random walk process,
Phys. Rev. E. 86,
011130 [9 pages] (2012).

Lecture Note
Lecture note on
reduced hierarchy equations of motion (Zip file, Oct. 10,
2015 version)
Program Codes:
 Markovian2005(GaussianMarkovian
master equation for a spin system coupled to 3D anisotropic baths) 
 nonMarkovian2009
(with low temperature correction terms 
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