2D Vib. Spectroscopy nonlinear optics Chemical Reaction Q. Thermodynamics 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]
bullet T. Ikeda and Y. Tanimura, Low-Temperature Quantum Fokker-Planck and Smoluchowski Equations and Their Extension to Multistate Systems, J. Chem. Theory Comput. 15 (2019). (Error correction)
bullet Y. Tanimura, Perspective: Numerically "Exact" Approach to Open Quantum Dynamics: The Hierarchical Equations of Motion (HEOM), J. Chem. Phys. 153, 020901 (2020). [Open Access]

Complete list of the related subject (applications of HEOM)

Lecture Note

bulletLecture note on reduced hierarchy equations of motion: Theory (Zip file, May 10, 2019)
bulletLecture note on reduced hierarchy equations of motion: Applications   (Zip file, May 10, 2019)

Program Codes

bulletMarkovian2005(Gaussian-Markovian master equation for a spin system coupled to 3D anisotropic baths)
bulletnonMarkovian2009 (with low temperature correction terms,   Jan 12, 2011 version)
bullet nonMarkovian2009+2D (with low temperature correction terms+ subroutines for linear and 2D correlation spectra,  Oct. 3rd, 2012 version)
bulletonMarkovian2012+2D (Drude+Brownian mode)
bulletTanimuranFP15 (real-time and imaginary-time quantum hierarchal Fokker-Planck equations,   March 21 , 2015 version)
bulletGPU-HEOM  (HEOM code for CUDA) M. Tsuchimoto and Y. Tanimura, J. Chem. Theory Comput.,11, 3859 (2015).
bullet Low-temperature corrected quantum Fokker-Planck and multi-state quantum Fokker-Planck Eqs. T. Ikeda and Y. Tanimura, J. Chem. Theory Comput. 15 (2019).

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