Quantum and classical Fokker-Planck equations for a Gaussian-Markovian noise bath

On the Quantum Correction For Thermodynamic Equilibrium

Wigner, E. (1932) · Physical Review · doi:10.1103/physrev.40.749 · Cited by 9,283

Fokker-Planck Equation

Risken, H. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-61544-3 · Cited by 9,128

Reaction-rate theory: fifty years after Kramers

Hänggi, P., Talkner, P., & Borkovec, M. (1990) · Reviews of Modern Physics · doi:10.1103/revmodphys.62.251 · Cited by 6,154

Transport, Collective Motion, and Brownian Motion

Mori, H. (1965) · Progress of Theoretical Physics · doi:10.1143/ptp.33.423 · Cited by 4,619

The theory of a general quantum system interacting with a linear dissipative system

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Path integral approach to quantum Brownian motion

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Quantum tunnelling in a dissipative system

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A Continued-Fraction Representation of the Time-Correlation Functions

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Nonlinear generalized Langevin equations

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Statistical mechanics of isomerization dynamics in liquids and the transition state approximation

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Semiclassical master equation in Wigners phase space applied to Brownian motion in a periodic potential

Coffey, W. T., Kalmykov, Y. P., Титов, С. В., & Mulligan, B. P. (2007) · Physical Review E · doi:10.1103/physreve.75.041117 · Cited by 30

Low-Temperature Quantum Fokker–Planck and Smoluchowski Equations and Their Extension to Multistate Systems

Ikeda, T., & Tanimura, Y. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b01195 · Cited by 30

Generalized quantum Fokker–Planck theory and its application to laser driven intramolecular hydrogen transfer reactions in condensed phases

Kühn, O., Zhao, Y. D., Shuang, F., & Yan, Y. (2000) · The Journal of Chemical Physics · doi:10.1063/1.481212 · Cited by 30

Exact open quantum system dynamics: Optimal frequency vs time representation of bath correlations

Hartmann, R., Werther, M., Großmann, F., & Strunz, W. T. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5097158 · Cited by 29

Exciton transfer in organic photovoltaic cells: A role of local and nonlocal electron–phonon interactions in a donor domain

Cainelli, M., & Tanimura, Y. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0036590 · Cited by 29

Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra

Ikeda, T., Dijkstra, A. G., & Tanimura, Y. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5086948 · Cited by 27

Proton tunneling in a two-dimensional potential energy surface with a non-linear system–bath interaction: Thermal suppression of reaction rate

Zhang, J., Borrelli, R., & Tanimura, Y. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0010580 · Cited by 27

Theory of electron transfer in the presence of dissipation

Zhang, M.-L., Zhang, S., & Pollak, E. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1623177 · Cited by 27

Two-dimensional vibrational spectroscopy of a double minimum system in a dissipative environment

Kühn, O., & Tanimura, Y. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1582841 · Cited by 27

Statistical quasi-particle theory for open quantum systems

Zhang, H.-D., Xu, R., Zheng, X. H., & Yan, Y. (2018) · Molecular Physics · doi:10.1080/00268976.2018.1431407 · Cited by 26

Energy Transfer across Nonpolar and Polar Contacts in Proteins: Role of Contact Fluctuations

Poudel, H., Reid, K. M., Yamato, T., & Leitner, D. M. (2020) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.0c08091 · Cited by 24

Theoretical study of photoinduced proton coupled electron transfer reaction using the non-perturbative hierarchical equations of motion method

Song, K., & Shi, Q. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4982928 · Cited by 23

Understanding the Large Kinetic Isotope Effect of Hydrogen Tunneling in Condensed Phases by Using Double-Well Model Systems

Liu, Y., Yan, Y., Xing, T., & Shi, Q. (2021) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.1c02851 · Cited by 23

An Approach to Quantum Transport Based on Reduced Hierarchy Equations of Motion: Application to a Resonant Tunneling Diode

Sakurai, A., & Tanimura, Y. (2013) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.82.033707 · Cited by 23

Energy-Level Diagrams and Their Contribution to Fifth-Order Raman and Second-Order Infrared Responses: Distinction between Relaxation Models by Two-Dimensional Spectroscopy

Okumura, K., & Tanimura, Y. (2003) · The Journal of Physical Chemistry A · doi:10.1021/jp027360o · Cited by 23

A simple improved low temperature correction for the hierarchical equations of motion

Fay, T. P. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0100365 · Cited by 22

Simulation of femtosecond “double-slit” experiments for a chromophore in a dissipative environment

Gelin, M. F., Tanimura, Y., & Domcke, W. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4832876 · Cited by 22

Quantum master equation in phase space: Application to the Brownian motion in a periodic potential

Coffey, W. T., Kalmykov, Y. P., Титов, С. В., & Mulligan, B. P. (2007) · Europhysics Letters (EPL) · doi:10.1209/0295-5075/77/20011 · Cited by 22

Pump-probe spectra and nuclear dynamics for a dissipative molecular system in a strong laser field: predissociation dynamics

Maruyama, Y., & Tanimura, Y. (1998) · Chemical Physics Letters · doi:10.1016/s0009-2614(98)00634-4 · Cited by 22

Photoinduced homogeneous proton-coupled electron transfer: Model study of isotope effects on reaction dynamics

Venkataraman, C., Soudackov, A. V., & Hammes‐Schiffer, S. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3249964 · Cited by 21

Open Quantum Dynamics Theory of Spin Relaxation: Application to μSR and Low-Field NMR Spectroscopies

Takahashi, H., & Tanimura, Y. (2020) · Journal of the Physical Society of Japan · doi:10.7566/jpsj.89.064710 · Cited by 20

Cavity quantum electrodynamics in the presence of energy relaxation and pure dephasing: A unified quantum master-equation approach

Xu, R., Yan, Y., & Li, X.-Q. (2002) · Physical Review A · doi:10.1103/physreva.65.023807 · Cited by 20

Numerically “exact” simulations of entropy production in the fully quantum regime: Boltzmann entropy vs von Neumann entropy

Sakamoto, S., & Tanimura, Y. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0033664 · Cited by 19

Unified time-path approach to the generating functional of the Brownian oscillator system: The bilinearly corrected Feynman rule for nonequilibrium processes

Okumura, K., & Tanimura, Y. (1996) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.53.214 · Cited by 19

Onsets of hierarchy truncation and self–consistent Born approximation with quantum mechanics prescriptions invariance

Zhang, H.-D., & Yan, Y. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4936831 · Cited by 18

Nonperturbative time-convolutionless quantum master equation from the path integral approach

Nan, G., Shi, Q., & Shuai, Z. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3108521 · Cited by 18

Exact quantum dissipative dynamics under external time-dependent driving fields

Xu, J., Xu, R., & Yan, Y. J. (2009) · New Journal of Physics · doi:10.1088/1367-2630/11/10/105037 · Cited by 18

Retardation effects in the dynamics of open molecular systems

Mančal, T., & May, V. (2001) · Chemical Physics · doi:10.1016/s0301-0104(01)00328-7 · Cited by 18

Mixed quantum classical calculation of proton transfer reaction rates: From deep tunneling to over the barrier regimes

Xie, W., Xu, Y., Zhu, L., & Shi, Q. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4873135 · Cited by 18

Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation

Alemi, M., & Loring, R. F. (2014) · The Journal of Physical Chemistry B · doi:10.1021/jp5076884 · Cited by 17

Solvent-induced polarization dynamics and coherent two-dimensional spectroscopy: Dissipaton equation of motion approach

Zhang, H.-D., Qiao, Q., Xu, R., & Yan, Y. (2016) · Chemical Physics · doi:10.1016/j.chemphys.2016.07.005 · Cited by 17

Spectral analysis of electron transfer kinetics. II

Jung, Y., & Cao, J. (2002) · The Journal of Chemical Physics · doi:10.1063/1.1491241 · Cited by 17

Quantum-classical approximation beyond Redfield theory

NEUFELD, A. A. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1587124 · Cited by 17

Discretized hierarchical equations of motion in mixed Liouville–Wigner space for two-dimensional vibrational spectroscopies of liquid water

Takahashi, H., & Tanimura, Y. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0135725 · Cited by 16

Memory Effects in the Fluorescence Depolarization Dynamics Studied within the B850 Ring of Purple Bacteria

Kleinekathöfer, U., Barvı́k, I., Heřman, P., Kondov, I., & Schreiber, M. (2003) · The Journal of Physical Chemistry B · doi:10.1021/jp035801d · Cited by 16

QuantumDynamics.jl: A modular approach to simulations of dynamics of open quantum systems

Bose, A. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0151483 · Cited by 15

An efficient approach to the quantum dynamics and rates of processes induced by natural incoherent light

Axelrod, S., & Brumer, P. W. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5041005 · Cited by 15

A variance reduction technique for the stochastic Liouville–von Neumann equation

Schmitz, K., & Stockburger, J. T. (2019) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2018-800094-y · Cited by 14

Open quantum dynamics of a three-dimensional rotor calculated using a rotationally invariant system-bath Hamiltonian: Linear and two-dimensional rotational spectra

Iwamoto, Y., & Tanimura, Y. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5108609 · Cited by 15

Realization of hierarchical equations of motion from stochastic perspectives

Wu, W. (2018) · Physical Review A · doi:10.1103/physreva.98.012110 · Cited by 14

Test of fluctuation theorems in non-Markovian open quantum systems

Kawamoto, T., & Hatano, N. (2011) · Physical Review E · doi:10.1103/physreve.84.031116 · Cited by 15

Phase Space Approach to Dissipative Molecular Dynamics

Kohen, D., & Tannor, D. J. (1999) · Advances in chemical physics · doi:10.1002/9780470141700.ch2 · Cited by 15

Erratum: “Two Dimensional Spectroscopy for Harmonic Vibrational Modes with Nonlinear System–Bath Interactions: I. Gaussian-White Case”

Steffen, T., & Tanimura, Y. (2007) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.76.078001 · Cited by 15

Open quantum systems with nonlinear environmental backactions: Extended dissipaton theory vs core-system hierarchy construction

Chen, Z., Wang, Y., Xu, R., & Yan, Y. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0134700 · Cited by 14

Thermodynamic quantum Fokker–Planck equations and their application to thermostatic Stirling engine

Koyanagi, S., & Tanimura, Y. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0225607 · Cited by 14

Collective bath coordinate mapping of “hierarchy” in hierarchical equations of motion

Ikeda, T., & Nakayama, A. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0082936 · Cited by 15

Quantum dynamics in a tiered non-Markovian environment

Fruchtman, A., Lovett, B. W., Benjamin, S. C., & Gauger, E. M. (2015) · New Journal of Physics · doi:10.1088/1367-2630/17/2/023063 · Cited by 15

Non-Markovian Quantum Dissipation in the Presence of External Fields

Xu, R., Mo, Y., Cui, P., Lin, S. H., & Yan, Y. (2003) · Progress in theoretical chemistry and physics · doi:10.1007/978-94-017-0635-3_2 · Cited by 14

Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability

Hyeon‐Deuk, K., & Tanimura, Y. (2005) · The Journal of Chemical Physics · doi:10.1063/1.2134702 · Cited by 14

On stability issues of the HEOM method

Krug, M., & Stockburger, J. T. (2023) · The European Physical Journal Special Topics · doi:10.1140/epjs/s11734-023-00972-9 · Cited by 13

A finite-difference implementation of the Caldeira–Leggett master equation

Großmann, F., & Koch, W. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3059006 · Cited by 13

Application of the imaginary time hierarchical equations of motion method to calculate real time correlation functions

Xing, T., Li, T., Yan, Y., Bai, S., & Shi, Q. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0095790 · Cited by 12

Application of the time-dependent projection operator technique: The nonlinear quantum master equation

Linden, O., & May, V. (1998) · Physica A Statistical Mechanics and its Applications · doi:10.1016/s0378-4371(98)00046-6 · Cited by 12

Nonlinear noninertial response of a quantum Brownian particle in a tilted periodic potential to a strong ac force as applied to a point Josephson junction

Coffey, W. T., Kalmykov, Y. P., Титов, С. В., & Cleary, L. (2009) · Physical Review B · doi:10.1103/physrevb.79.054507 · Cited by 12

Non-Markovian entanglement sudden death and rebirth of a two-qubit system in the presence of system-bath coherence

Wang, H.-T., Li, C., Zou, Y., Ge, R.-C., & Guo, G. (2011) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2011.04.029 · Cited by 11

Towards an understanding of escape rate and state dependent diffusion for a quantum dissipative system

Shit, A., Chattopadhyay, S., & Chaudhuri, J. R. (2011) · Chemical Physics · doi:10.1016/j.chemphys.2011.06.002 · Cited by 11

Two-Time Correlation Function of a Two-Dimensional Quantal Rotator in a Colored Noise

Suzuki, Y., & Tanimura, Y. (2002) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.71.2414 · Cited by 11

Partition function of a particle coupled to an arbitrary heat bath in the quasienergy representation for the path integral

Benderskii, V. A., & Makarov, D. E. (1992) · Physics Letters A · doi:10.1016/0375-9601(92)91088-9 · Cited by 11

Exciton dissociation in the presence of phonons: A reduced hierarchy equations of motion approach

Yao, Y., Yang, W., & Zhao, Y. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4867418 · Cited by 10

Classical and quantum thermodynamics in a non-equilibrium regime: Application to thermostatic Stirling engine

Koyanagi, S., & Tanimura, Y. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0220685 · Cited by 10

Hierarchical quantum master equation approach to charge transport in molecular junctions with time-dependent molecule-lead coupling strengths

Erpenbeck, A., Götzendörfer, L., Schinabeck, C., & Thoss, M. (2019) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2018-800083-0 · Cited by 10

A dynamic mean-field theory for dissipative interacting many-electron systems

Yokojima, S., Chen, G., Xu, R., & Yan, Y. (2003) · Chemical Physics Letters · doi:10.1016/s0009-2614(02)02048-1 · Cited by 10

Non-Markovian entanglement dynamics of open quantum systems with continuous measurement feedback

Jiang, W., Wu, F.-Z., & Yang, G. (2018) · Physical Review A · doi:10.1103/physreva.98.052134 · Cited by 10

Non-Markovian dynamics of the mixed-state geometric phase of dissipative qubits

Guo, W., Ma, J., Yin, X., Zhong, W., & Wang, X. (2014) · Physical Review A · doi:10.1103/physreva.90.062133 · Cited by 8

Closures of the functional expansion hierarchy in the non-Markovian quantum state diffusion approach

Ritschel, G., Strunz, W. T., & Eisfeld, A. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4986251 · Cited by 8

Recent advances in fermionic hierarchical equations of motion method for strongly correlated quantum impurity systems

Cao, J., Ye, L., Xu, R., Zheng, X. H., & Yan, Y. (2023) · JUSTC · doi:10.52396/justc-2022-0164 · Cited by 9

Geometric phase accumulated in a driven quantum system coupled to a structured environment

Villar, P. I., & Soba, A. (2020) · Physical Review A · doi:10.1103/physreva.101.052112 · Cited by 9

Open system dynamics approach to polyatomic molecules: Excitons in chromophore complexes

May, V. (2006) · International Journal of Quantum Chemistry · doi:10.1002/qua.21181 · Cited by 9

Optimized perturbation approach with a Legendre transformation to a dissipative system: Correlation functions of a Morse oscillator

Suzuki, Y., & Tanimura, Y. (1999) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.59.1475 · Cited by 9

Quantum Stochastic Dynamics in the Presence of a Time-Periodic Rapidly Oscillating Potential: Nonadiabatic Escape Rate

Shit, A., Chattopadhyay, S., & Chaudhuri, J. R. (2013) · The Journal of Physical Chemistry A · doi:10.1021/jp402565y · Cited by 9

Simulating many-body open quantum systems by harnessing the power of artificial intelligence and quantum computing

Ye, L., Wang, Y., & Zheng, X. H. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0242648 · Cited by 9

Phase induced transport of a Brownian particle in a periodic potential in the presence of an external noise: A semiclassical treatment

Bhattacharya, S., Chattopadhyay, S., Chaudhury, P., & Chaudhuri, J. R. (2011) · Journal of Mathematical Physics · doi:10.1063/1.3614776 · Cited by 7

Quantum hierarchical Fokker–Planck equations with U(1) gauge fields: Application to the Aharonov–Bohm ring

Yang, H., Koyanagi, S., & Tanimura, Y. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0296839 · Cited by 6

Dissipaton dynamics theory versus quantum master equations

Wang, Y., Pan, Z. J., Zhang, H.-D., & Yan, Y. J. (2018) · Chemical Physics · doi:10.1016/j.chemphys.2018.08.046 · Cited by 6

Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath

Přáda, A., Pós, E. S., & Althorpe, S. C. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0138250 · Cited by 6

Classical and quantum thermodynamics described as a system–bath model: The dimensionless minimum work principle

Koyanagi, S., & Tanimura, Y. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0205771 · Cited by 6

Quantum effects in intermediate-temperature dipole-dipole correlation-functions in the presence of an environment

Großmann, F. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4896835 · Cited by 6

A semiclassical approach to explore the bistable kinetics of a Brownian particle in a nonequilibrium environment

Ghosh, P., Shit, A., Chattopadhyay, S., & Chaudhuri, J. R. (2011) · Journal of Statistical Mechanics Theory and Experiment · doi:10.1088/1742-5468/2011/02/p02026 · Cited by 6

Derivation of quantum kinetic equation from the Liouville-von Neumann equation

Bondarev, B. V. (1994) · Theoretical and Mathematical Physics · doi:10.1007/bf01017320 · Cited by 6

Hierarchical Equations-of-Motion Method for Momentum System–Bath Coupling

Gelin, M. F., Borrelli, R., & Chen, L. (2021) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.1c02431 · Cited by 5

How proton transfer impacts hachimoji DNA

Warman, H., Slocombe, L., & Sacchi, M. (2023) · RSC Advances · doi:10.1039/d3ra00983a · Cited by 5

Mean-Field Ring Polymer Rates Using a Population Dividing Surface

London, N., Bu, S., Johnson, B., & Ananth, N. (2024) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.4c00005 · Cited by 5

Taming the escape dynamics of nonadiabatic time-periodically driven quantum dissipative system within the frame of Wigner formalism

Shit, A., Chattopadhyay, S., & Chaudhuri, J. R. (2014) · Chemical Physics · doi:10.1016/j.chemphys.2014.01.008 · Cited by 5

Phase-space description of a particle in a quartic double-well potential

Ceausu–Velcescu, A., Blaise, P., & Kalmykov, Y. P. (2014) · International Journal of Modern Physics B · doi:10.1142/s0217979214501641 · Cited by 5

Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Iwamoto, Y., & Tanimura, Y. (2021) · Journal of Computational Electronics · doi:10.1007/s10825-021-01754-z · Cited by 5

Development of a semiclassical method to compute mobility and diffusion coefficient of a Brownian particle in a nonequilibrium environment

Shit, A., Ghosh, P., Chattopadhyay, S., & Chaudhuri, J. R. (2011) · Physical Review E · doi:10.1103/physreve.83.031125 · Cited by 5

SPIN RELAXATION IN PHASE SPACE

Kalmykov, Y. P., Coffey, W. T., & Титов, С. В. (2016) · Advances in chemical physics · doi:10.1002/9781119290971.ch2 · Cited by 5

A tensor network representation of path integrals: Implementation and analysisPreprint

Bose, A., & Walters, P. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2106.12523 · Cited by 5

Schwinger–Keldysh nonperturbative field theory of open quantum systems beyond the Markovian regime: application to spin-boson and spin-chain-boson models

Reyes-Osorio, F., Garcia-Gaitan, F., Strachan, D. J., Plecháč, P., Clark, S. R. L., & Nikolić, B. K. (2025) · Reports on Progress in Physics · doi:10.1088/1361-6633/ae2888 · Cited by 4

Computable form of the Born-Markov master equation for open multilevel quantum systems

Liang, X.-T. (2019) · Physical Review A · doi:10.1103/physreva.99.022118 · Cited by 4

Computational characterization of nanosystems

Zeng, X., Hu, W., Zheng, X. H., Zhao, J., Li, Z., & Yang, J. (2022) · Chinese Journal of Chemical Physics · doi:10.1063/1674-0068/cjcp2111233 · Cited by 4

Quantum decoherence dynamics in stochastically fluctuating environments

Cai, X.-J., Feng, Y., Ren, J., Peng, Y., & Zheng, Y. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0217863 · Cited by 4

Enhancement of quantum correlations and a geometric phase for a driven bipartite quantum system in a structured environment

Villar, P. I., & Soba, A. (2021) · Physical Review A · doi:10.1103/physreva.103.032222 · Cited by 4

Time-Local Quantum Master Equations and their Applications to Dissipative Dynamics and Molecular Wires

Kleinekathöfer, U. (2009) · Springer series in chemical physics · doi:10.1007/978-3-642-02306-4_10 · Cited by 4

The Lindblad and Redfield forms derived from the Born–Markov master equation without secular approximation and their applications

Liao, C.-Y., & Liang, X.-T. (2021) · Communications in Theoretical Physics · doi:10.1088/1572-9494/abec65 · Cited by 4

Non-Markovian theory of open systems in classical limit

NEUFELD, A. A. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1769353 · Cited by 4

Modeling dissipation in quantum active matter

Antonov, A. P., Lee, S., Liebchen, B., Löwen, H., Melles, J., Morigi, G., Tuchkov, Y., & Vrugt, M. T. (2026) · Physical Review A · doi:10.1103/4gyc-3pht · Cited by 3

System–bath modeling in vibrational spectroscopy via molecular dynamics: A machine learning framework for hierarchical equations of motion (HEOM)

Park, K., Yoon, J.-Y., & Tanimura, Y. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0300203 · Cited by 3

Quantum hierarchical Fokker–Planck equations with U(1) gauge fields [U(1)-QHFPE]: A computational framework for Aharonov–Bohm effects

Koyanagi, S., Yang, H., & Tanimura, Y. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0302697 · Cited by 3

Adjoint-Based Calibration of Nonlinear Stochastic Differential Equations

Bartsch, J., Denk, R., & Volkwein, S. (2024) · Applied Mathematics & Optimization · doi:10.1007/s00245-024-10181-y · Cited by 3

Fokker—Planck Equations and Stochastic Differential Equations

Carmichael, H. J. (1999) · Springer eBooks · doi:10.1007/978-3-662-03875-8_5 · Cited by 3

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions

Banik, S. K., Bag, B. C., & Ray, D. S. (2002) · Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics · doi:10.1103/physreve.65.051106 · Cited by 40

Semiclassical description of harmonic quantal Brownian motion

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Quantum Fokker-Planck equation for interacting waves

Sinclair, R., Putterman, S., & Roberts, P. H. (1996) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.1996.0038

Brownian Motion of a Quantum Oscillator

Agarwal, G. S. (1971) · Physical Review A · doi:10.1103/physreva.4.739 · Cited by 208