A unified view of hierarchy approach and formula of differentiation

Yan, Yun-An; Wang, Haobin; Shao, Jiushu

doi:10.1063/1.5126341

Title: A unified view of hierarchy approach and formula of differentiation

Authors:

^[1];

^[2]; Shao, Jiushu ^[3]

School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China
Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA and Beijing Computational Science Research Center, No. 10 East Xibeiwang Road, Haidian District, Beijing 100193, China
College of Chemistry and Center for Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China

Publication Date:: 2019-10-28

Sponsoring Org.:: USDOE

OSTI Identifier:: 1571839

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Publisher's Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Name: Journal of Chemical Physics Journal Volume: 151 Journal Issue: 16; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics

Country of Publication:: United States

Language:: English

Citation Formats


                    Yan, Yun-An, Wang, Haobin, and Shao, Jiushu. A unified view of hierarchy approach and formula of differentiation.  United States: N. p., 2019. 
Web.  doi:10.1063/1.5126341.

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                    Yan, Yun-An, Wang, Haobin, & Shao, Jiushu. A unified view of hierarchy approach and formula of differentiation.  United States.  https://doi.org/10.1063/1.5126341

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                    Yan, Yun-An, Wang, Haobin, and Shao, Jiushu. Mon .  
"A unified view of hierarchy approach and formula of differentiation".  United States.  https://doi.org/10.1063/1.5126341.

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@article{osti_1571839,

  title        = {A unified view of hierarchy approach and formula of differentiation},

  author       = {Yan, Yun-An and Wang, Haobin and Shao, Jiushu},

  abstractNote = {},

  doi          = {10.1063/1.5126341},

  journal      = {Journal of Chemical Physics},

  number       = 16,

  volume       = 151,

  place        = {United States},

  year         = {2019},

  month        = {10}

}

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Title: A unified view of hierarchy approach and formula of differentiation

Citation Formats

The density-matrix renormalization group in the age of matrix product states journal, January 2011

Generation of Colored Noise journal, July 2001

Efficient propagation of the hierarchical equations of motion using the matrix product state method journal, May 2018

Decoupling quantum dissipation interaction via stochastic fields journal, March 2004

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Perturbation expansions of stochastic wavefunctions for open quantum systems journal, November 2017

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Linear quantum state diffusion for non-Markovian open quantum systems journal, December 1996

Dynamics of the dissipative two-state system journal, January 1987

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Stochastic Liouville Equations journal, February 1963

Stochastic description of quantum Brownian dynamics journal, May 2016

A novel method for simulating quantum dissipative systems journal, March 1996

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Hierarchical approach based on stochastic decoupling to dissipative systems journal, September 2004

“Formulae of differentiation” and their use for solving stochastic equations journal, May 1978

Open System Dynamics with Non-Markovian Quantum Trajectories journal, March 1999

Time evolution of Matrix Product States journal, December 2006

Exact c -Number Representation of Non-Markovian Quantum Dissipation journal, April 2002

On the statistical theory of electromagnetic waves in a fluctuating medium (I) journal, May 1963

Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics journal, June 2017

Dynamical Simulation of Current Fluctuations in a Dissipative Two-State System journal, March 1998

From coherent motion to localization: dynamics of the spin-boson model at zero temperature journal, November 2008

The quantum-state diffusion model applied to open systems journal, November 1992

Quantum tunnelling in a dissipative system journal, September 1983

Stochastic integral journal, January 1944

Efficient hierarchical Liouville space propagator to quantum dissipative dynamics journal, February 2009

Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146 , 530–533 (1908)] journal, November 1997

Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen journal, January 1905

Numerical method for colored-noise generation and its application to a bistable system journal, December 1990

Rigorous representation and exact simulation of real Gaussian stationary processes journal, October 2010

Simulation of Stationary Gaussian Processes in [0,1] d journal, December 1994

From coherent motion to localization: II. Dynamics of the spin-boson model with sub-Ohmic spectral density at zero temperature journal, May 2010

The density-matrix renormalization group in the age of matrix product states
journal, January 2011

Generation of Colored Noise
journal, July 2001

Efficient propagation of the hierarchical equations of motion using the matrix product state method
journal, May 2018

Decoupling quantum dissipation interaction via stochastic fields
journal, March 2004

Hierarchy of forward-backward stochastic Schrödinger equation
journal, July 2016

Perturbation expansions of stochastic wavefunctions for open quantum systems
journal, November 2017

The Pricing of Options and Corporate Liabilities
journal, May 1973

Hermitian non-Markovian stochastic master equations for quantum dissipative dynamics
journal, August 2015

Linear quantum state diffusion for non-Markovian open quantum systems
journal, December 1996

Dynamics of the dissipative two-state system
journal, January 1987

The theory of a general quantum system interacting with a linear dissipative system
journal, October 1963

Stochastic Liouville Equations
journal, February 1963

Stochastic description of quantum Brownian dynamics
journal, May 2016

A novel method for simulating quantum dissipative systems
journal, March 1996

Quantum Dissipative Systems
book, March 2012

Hierarchical approach based on stochastic decoupling to dissipative systems
journal, September 2004

“Formulae of differentiation” and their use for solving stochastic equations
journal, May 1978

Open System Dynamics with Non-Markovian Quantum Trajectories
journal, March 1999

Time evolution of Matrix Product States
journal, December 2006

Exact $c$ -Number Representation of Non-Markovian Quantum Dissipation
journal, April 2002

On the statistical theory of electromagnetic waves in a fluctuating medium (I)
journal, May 1963

Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics
journal, June 2017

Dynamical Simulation of Current Fluctuations in a Dissipative Two-State System
journal, March 1998

From coherent motion to localization: dynamics of the spin-boson model at zero temperature
journal, November 2008

The quantum-state diffusion model applied to open systems
journal, November 1992

Quantum tunnelling in a dissipative system
journal, September 1983

Stochastic integral
journal, January 1944

Efficient hierarchical Liouville space propagator to quantum dissipative dynamics
journal, February 2009

Paul Langevin’s 1908 paper “On the Theory of Brownian Motion” [“Sur la théorie du mouvement brownien,” C. R. Acad. Sci. (Paris) 146 , 530–533 (1908)]
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journal, January 1905

Numerical method for colored-noise generation and its application to a bistable system
journal, December 1990

Rigorous representation and exact simulation of real Gaussian stationary processes
journal, October 2010

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From coherent motion to localization: II. Dynamics of the spin-boson model with sub-Ohmic spectral density at zero temperature
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