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Cited by 131Spectroscopy and Quantum Chemical StudiesAdvanced Thermodynamics and Statistical MechanicsQuantum Mechanics and Applications

A hybrid stochastic hierarchy equations of motion approach to treat the low temperature dynamics of non-Markovian open quantum systems

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Moix, Jeremy M., Cao, Jianshu·2013·The Journal of Chemical Physics
DOI 10.1063/1.4822043
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Abstract

The hierarchical equations of motion technique has found widespread success as a tool to generate the numerically exact dynamics of non-Markovian open quantum systems. However, its application to low temperature environments remains a serious challenge due to the need for a deep hierarchy that arises from the Matsubara expansion of the bath correlation function. Here we present a hybrid stochastic hierarchical equation of motion (sHEOM) approach that alleviates this bottleneck and leads to a numerical cost that is nearly independent of temperature. Additionally, the sHEOM method generally converges with fewer hierarchy tiers allowing for the treatment of larger systems. Benchmark calculations are presented on the dynamics of two level systems at both high and low temperatures to demonstrate the efficacy of the approach. Then the hybrid method is used to generate the exact dynamics of systems that are nearly impossible to treat by the standard hierarchy. First, exact energy transfer rates are calculated across a broad range of temperatures revealing the deviations from the Förster rates. This is followed by computations of the entanglement dynamics in a system of two qubits at low temperature spanning the weak to strong system-bath coupling regimes.

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  • If the stochastic processes are real, the Lα operators are Hermitian and the resulting dissipator is unital, leading to monotonic decay of purity.

    “Notice that, if the stochastic processes are taken to be real from the beginning (η 00 α ðtÞ ¼ 0), the Lα operators in (2) then fulfill Hermiticity.”

    From Quantum simulation of generic many-body open system dynamics using classical noise (2017) · cites this paper as [35]

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  1. L. S. Schulman, Techniques and Applications of Path Integration (Wiley, New York, 1986).

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Authors
Moix, J. M., & Cao, J.
Affiliations
Massachusetts Institute of Technology (US)
ORCID
Venue
The Journal of Chemical Physics
Publisher
AIP Publishing
Published
2013-10-02
Volume
139
Issue
13
Pages
134106-134106
ISSN
  • 0021-9606 (ISSN-L)
  • 1089-7690
DOI
10.1063/1.4822043
OpenAlex
W2198713534
Cited by
131
References
34
Citations by year
2026: 6 · 2025: 7 · 2024: 10 · 2023: 5 · 2022: 11 · 2021: 9 · 2020: 5 · 2019: 12 · 2018: 19 · 2017: 18 · 2016: 7 · 2015: 14 · 2014: 8
FWCI
4.98
Type
journal article
Language
en
Open access
Locations
  • The Journal of Chemical Physics (publishedVersion)
  • PubMed (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • National Science Foundation (1112825)
  • U.S. Department of Energy (DESC0001088)
  • Defense Advanced Research Projects Agency (N99001-10- 1-4063)
  • Office of Science (DESC0001088)
  • Advanced Research Projects Agency
  • Division of Chemistry (CHE-1112825)
  • Basic Energy Sciences (DE-SC0001088)
Topics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Spectroscopy and Quantum Chemical Studies
  • Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
Keywords
low-temperature dynamics, bath correlation functions, two-level system, fluorescence resonance energy transfer, entanglement dynamics, qubits, system-bath coupling

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