2D Spectroscopy nonlinear optics Chemical Reaction quantum transport Frustrated systems Organic conductors HEOM Path Integrals Molecular Dynamics Stochastic Theory Monte Carlo quantum chemistry

Hierarchy equations approach to quantum dissipative dynamics

bulletDerivation of hierarchal equations of motion (master equation and Fokker-Planck equation)
bulletInclusion of low temperature correction terms
bulletDerivation of multistate quantum Fokker-Planck equation and its applications
bulletInitial system-bath coherence and imaginary HEOM

Representative references

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). [OPEN SELECT]
bulletY. Tanimura and P. G. Wolynes, Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath, Phys. Rev. A43, 4131-4142 (1991).
bullet Y. Tanimura, Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath, Phys. Rev. A41, 6676-6687 (1990).
bullet Y. Tanimura and Y. Maruyama, Gaussian-Markovian quantum Fokker-Planck approach to nonlinear spectroscopy of a displaced Morse potentials system: dissociation, predissociation and optical Stark effects, J. Chem. Phys. 107, 1779-1793 (1997).
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]
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]

Lecture Note

Lecture note on reduced hierarchy equations of motion (Zip file, NOV. 25, 2016)

Program Codes

bulletMarkovian2005(Gaussian-Markovian master equation for a spin system coupled to 3D anisotropic baths)
bulletnonMarkovian2009 (with low temperature correction terms,  June. 22nd, 2010 version)
bullet nonMarkovian2009+2D (with low temperature correction terms+ subroutines for linear and 2D correlation spectra,  Oct. 3rd, 2012 version)
bullet nonMarkovian2012+2D (Drude+Brownian mode)
bulletTanimuranFP15 (real-time and imaginary-time quantum hierarchal Fokker-Planck equations,   March 21 , 2015 version)

Complete list of the related subject (applications of HEOM)

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