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Stochastic Formalism and Simulation of Quantum Dissipative Dynamics Cao, Jianshu
Description
Our starting point is a stochastic decomposition scheme to study dissipative dynamics of an open system. In this scheme, any two-body interactions between constituents of the quantum system can be decoupled with a common white noise that acts on the two individual subsystems. $$ $$ (I) Using the decomposition scheme, we obtain a stochasticâ differential equation, which reduces to generalized hierarchical equations of motion (GHEOM) and thus represents a unified treatment of boson, fermion, and spin baths.[1] Applications of GHEOM to spin baths confirm the scaling relation that maps spin baths to boson baths and characterizes anharmonic effects often associated with low-frequency or strong coupling spin modes. [2] $$ $$ (II) The decomposition scheme also leads to the stochastic path integral approach, which directly simulates quantum dissipation with complex noise. The approach is applied successfully to obtain the equilibrium density matrix, multichomophoric spectra, and Forster energy transfer rate. [3] For real time propagation, we demonstrate the advantages of combining stochastic path integrals, deterministic quantum master equations [4], and possibly the transfer tensor method [5]. $$ $$ [1] A unified stochastic formalism of quantum dissipation: I. Generalized Hierarchical equation, Hsien and Cao, JCP 148, p014103 (2018) $$ $$ [2] A unified stochastic formalism of quantum dissipation: II. Beyond linear response of spin baths. Hsien and Cao, JCP 148, p014104 (2018) $$ $$ [3] Equilibrium-reduced density matrix formulation: Influence of noise, disorder, and temperature on localization in excitonic systems. J. Moix, Y. Zhao, and J. Cao, Phys. Rev. B 85, 115412 (2012) $$ $$ [4] A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems. J. M. Moix and J. Cao, J. Chem. Phys. 139, 134106 (2013) $$ $$ [5] Non-Markovian dynamical maps: Numerical processing of open quantum trajectories. J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)
Item Metadata
Title |
Stochastic Formalism and Simulation of Quantum Dissipative Dynamics
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2019-08-23T10:14
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Description |
Our starting point is a stochastic decomposition scheme to study dissipative
dynamics of an open system. In this scheme, any two-body interactions between
constituents of the quantum system can be decoupled with a common white
noise that acts on the two individual subsystems.
$$
$$
(I) Using the decomposition scheme, we obtain a stochasticâ differential
equation, which reduces to generalized hierarchical equations of
motion (GHEOM) and thus represents a unified treatment of boson,
fermion, and spin baths.[1] Applications of GHEOM to spin baths
confirm the scaling relation that maps spin baths to boson baths and
characterizes anharmonic effects often associated with low-frequency
or strong coupling spin modes. [2]
$$
$$
(II) The decomposition scheme also leads to the stochastic path integral
approach, which directly simulates quantum dissipation with complex
noise. The approach is applied successfully to obtain the equilibrium
density matrix, multichomophoric spectra, and Forster energy transfer
rate. [3] For real time propagation, we demonstrate the advantages of
combining stochastic path integrals, deterministic quantum master
equations [4], and possibly the transfer tensor method [5].
$$
$$
[1] A unified stochastic formalism of quantum dissipation: I. Generalized
Hierarchical equation, Hsien and Cao, JCP 148, p014103 (2018)
$$
$$
[2] A unified stochastic formalism of quantum dissipation: II. Beyond linear
response of spin baths. Hsien and Cao, JCP 148, p014104 (2018)
$$
$$
[3] Equilibrium-reduced density matrix formulation: Influence of noise, disorder,
and temperature on localization in excitonic systems. J. Moix, Y. Zhao, and J.
Cao, Phys. Rev. B 85, 115412 (2012)
$$
$$
[4] A hybrid stochastic hierarchy equations of motion approach to treat the low
temperature dynamics of non-Markovian open quantum systems. J. M. Moix and
J. Cao, J. Chem. Phys. 139, 134106 (2013)
$$
$$
[5] Non-Markovian dynamical maps: Numerical processing of open quantum
trajectories. J. Cerrillo and J. Cao, Phys. Rev. Lett. 112, 110401 (2014)
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Extent |
38.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Massachusetts Institute of Technology
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Series | |
Date Available |
2020-09-06
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0394214
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International