Non-Markovian dynamics of a qubit coupled to an Ising spin bath
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We study the analytically solvable Ising model of a single qubit system coupled to a spin bath. The purpose of this study is to analyze and elucidate the performance of Markovian and non-Markovian master equations describing the dynamics of the system qubit, in comparison to the exact solution. We find that the time-convolutionless master equation performs particularly well up to fourth order in the system-bath coupling constant, in comparison to the Nakajima-Zwanzig master equation. Markovian approaches fare poorly due to the infinite bath correlation time in this model. A recently proposed post-Markovian master equation performs comparably to the time-convolutionless master equation for a properly chosen memory kernel, and outperforms all the approximation methods considered here at long times. Our findings shed light on the applicability of master equations to the description of reduced system dynamics in the presence of spin baths.
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The converse of the statement that non-Markovian processes are non-divisible is not true: there exist non-divisible dynamical processes which are Markovian in the sense of the paper's definition.
“However, it is important to note that the converse of this statement is not true, i.e., there exist non-divisible dynamical processes which are Markovian in the sense of the above definition.”
From Foundations and measures of quantum non-Markovianity (2012) · cites this paper as [37]
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Tiwari, D., & Banerjee, S. (2026) · The Journal of Chemical Physics · doi:10.1063/5.0323945
- Authors
- Krovi, H., Oreshkov, O., Ryazanov, M., & Lidar, D. A.
- Affiliations
- University of Southern California (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2007-11-28
- Volume
- 76
- Issue
- 5
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2024687873
- Cited by
- 70
- References
- 46
- Citations by year
- 2026: 2 · 2025: 5 · 2024: 3 · 2022: 3 · 2021: 5 · 2020: 3 · 2019: 1 · 2018: 3 · 2017: 5 · 2016: 2 · 2015: 1 · 2014: 2 · 2013: 7 · 2012: 4
- FWCI
- 2.86
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- non-Markovian dynamics, qubits, time-convolutionless master equation, memory kernel, system-bath coupling, reduced dynamics, open quantum systems, exact solutions
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