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Title: Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes

Abstract

We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.

Authors:
; ; ;  [1]
  1. Beijing National Laboratory for Molecular Sciences, State Key Laboratory for Structural Chemistry of Unstable and Stable Species, Institute of Chemistry, Chinese Academy of Sciences, Zhongguancun, Beijing 100190 (China)
Publication Date:
OSTI Identifier:
22253316
Resource Type:
Journal Article
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 140; Journal Issue: 13; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABSORPTION; COMPUTERIZED SIMULATION; CORRELATION FUNCTIONS; DECOMPOSITION; DENSITY; DIMERS; EQUATIONS OF MOTION; HARMONIC OSCILLATORS; INTERMEDIATE COUPLING; PERTURBATION THEORY; SPECTRAL DENSITY

Citation Formats

Liu, Hao, Zhu, Lili, Bai, Shuming, and Shi, Qiang. Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes. United States: N. p., 2014. Web. doi:10.1063/1.4870035.
Liu, Hao, Zhu, Lili, Bai, Shuming, & Shi, Qiang. Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes. United States. https://doi.org/10.1063/1.4870035
Liu, Hao, Zhu, Lili, Bai, Shuming, and Shi, Qiang. Mon . "Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes". United States. https://doi.org/10.1063/1.4870035.
@article{osti_22253316,
title = {Reduced quantum dynamics with arbitrary bath spectral densities: Hierarchical equations of motion based on several different bath decomposition schemes},
author = {Liu, Hao and Zhu, Lili and Bai, Shuming and Shi, Qiang},
abstractNote = {We investigated applications of the hierarchical equation of motion (HEOM) method to perform high order perturbation calculations of reduced quantum dynamics for a harmonic bath with arbitrary spectral densities. Three different schemes are used to decompose the bath spectral density into analytical forms that are suitable to the HEOM treatment: (1) The multiple Lorentzian mode model that can be obtained by numerically fitting the model spectral density. (2) The combined Debye and oscillatory Debye modes model that can be constructed by fitting the corresponding classical bath correlation function. (3) A new method that uses undamped harmonic oscillator modes explicitly in the HEOM formalism. Methods to extract system-bath correlations were investigated for the above bath decomposition schemes. We also show that HEOM in the undamped harmonic oscillator modes can give detailed information on the partial Wigner transform of the total density operator. Theoretical analysis and numerical simulations of the spin-Boson dynamics and the absorption line shape of molecular dimers show that the HEOM formalism for high order perturbations can serve as an important tool in studying the quantum dissipative dynamics in the intermediate coupling regime.},
doi = {10.1063/1.4870035},
url = {https://www.osti.gov/biblio/22253316}, journal = {Journal of Chemical Physics},
issn = {0021-9606},
number = 13,
volume = 140,
place = {United States},
year = {2014},
month = {4}
}