Stochastic theory

bulletStudies of second order optical processes of multistate system by stochastic theory
bulletDerive the Gaussian-Markovian quantum master equation to generalize the stochastic Liouville equation.
bulletFractal noise
bulletNon-Gaussian processes

Representative references

bulletY. Tanimura, H. Takano, and R. Kubo, Second order optical processes of a randomly modulated multi-level atom, J. Phys. Soc. Jpn. 55, 4550-4565 (1986).
bulletY. Tanimura and R. Kubo, Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 101-114 (1989). pdf file (1541k) [full text PDF: OPEN SELECT]
bulletY. Tanimura, T. Suzuki and R. Kubo, Second order optical process of a three-level system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 1850-1859 (1989).
bulletY. Tanimura, Stochastic Liouville, Langevin, Fokker-Planck, and master equation approaches to quantum dissipative systems, J. Phys. Soc. Jpn.  75,  082001  (2006). [full text PDF: OPEN SELECT]
bullet G. Gangopadhyay, S. Ghoshal, and Yoshitaka Tanimura, A thermal bath induced new resonance in linear and nonlinear spectra of two-level systems, Chem. Phys. 242, 367-385 (1999).
bullet D. Packwood and Y. Tanimura, Non-Gaussian stochastic dynamics of spins and oscillators, Phys. Rev. E 84, 061111 [9pages] (2011)
bullet D. Packwood and Y. Tanimura, Dephasing by a continuous-time random walk process, Phys. Rev. E. 86, 011130 [9 pages] (2012).

　

Lecture Note
bulletLecture note on reduced hierarchy equations of motion: Theory (Zip file, March 25 2025)
bulletLecture note on reduced hierarchy equations of motion: Applications   (Zip file, March 25 2025)

Lecture Mpegs

bulletQuantum noise cannot be Markovian: Hierarchical equations of motion approach: PART I (Intensive Lectures)
bulletQuantum noise cannot be Markovian: Hierarchical equations of motion approach: PART II (Seminars)
bulletNonequilibrium thermodynamics described as state variables (MPEG 185M) (PPT lecture note)
bulletNumerically “exact” approach to open quantum dynamics: The hierarchical equations of motion (HEOM) (Mpeg 661M)- at ISSP 2023.10.7 &12  

　

Program Codes:

bulletMarkovian2005(Gaussian-Markovian master equation for a spin system coupled to 3D anisotropic baths)
bulletnonMarkovian2009 (with low temperature correction terms

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