Hierarchical equations
of motion approach to quantum dissipative dynamics
 | Derivation of hierarchal equations of motion (master equation and
Fokker-Planck equation) |
| Inclusion of low temperature correction terms |
| Derivation of multistate quantum Fokker-Planck equation and its
applications |
| Initial system-bath coherence and imaginary HEOM |
Representative references
|
| Y. 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]
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| Y. Tanimura and P. G. Wolynes, Quantum and classical
Fokker-Planck equations for a Gaussian-Markovian noise bath,
Phys. Rev. A43,
4131-4142 (1991). |
|
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Y. Tanimura, Nonperturbative expansion method for a
quantum system coupled to a harmonic-oscillator bath,
Phys.
Rev. A41, 6676-6687 (1990).
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|
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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).
|
|
| Y. 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]
|
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| 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] |
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Y. Tanimura, Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations,
J. Chem. Phys.
142, 144110 [20 pages] (2015)
(PDF)
[Open Access] |
|
| 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)
|
|
| 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
Lecture Mpegs
Program Codes
| Markovian2005(Gaussian-Markovian
master equation for a spin system coupled to 3D anisotropic baths) |
| nonMarkovian2009
(with low temperature correction terms, Jan 12, 2011 version) |
|
nonMarkovian2009+2D (with low temperature correction terms+ subroutines
for linear and 2D correlation spectra, Oct. 3rd, 2012 version) |
| onMarkovian2012+2D
(Drude+Brownian mode) |
| TanimuranFP15 (real-time and imaginary-time quantum hierarchal
Fokker-Planck equations, March 21 , 2015 version) |
| GPU-HEOM (HEOM code
for CUDA)
M. Tsuchimoto and Y.
Tanimura, J. Chem. Theory Comput.,11, 3859 (2015). |
|
Low-temperature corrected quantum Fokker-Planck and multi-state quantum
Fokker-Planck Eqs. T. Ikeda and Y. Tanimura, J. Chem. Theory Comput. 15
(2019). |
|
S. Koyanagi and Y. Tanimura, Classical and
quantum thermodynamics in a non-equilibrium regime: Application to
thermostatic Stirling engine,
J. Chem. Phys.
161, 114113 (2024).(PDF) |
|
Thermodynamic Quantum Fokker-Planck Equation
(T-QFPE). Ver, 1,1 (Oct. 21, 2024);S. Koyanagi and Y. Tanimura, J. Chem. Phys.
161, 112501 (2024).(PDF)ierarchical
Equations of Motion for the Multiple Baths (HEOM-MB). Ver. 1.0 (Oct. 17, 2024);
J. Chem. Phys.
161, 162501 (2024).(PDF) |
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