Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911439979020288 |
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| author | Liu, Wei Bi, Rui-Hao Su, Yu Xu, Limin Zhou, Zhennan Wang, Yao Dou, Wenjie |
| author_facet | Liu, Wei Bi, Rui-Hao Su, Yu Xu, Limin Zhou, Zhennan Wang, Yao Dou, Wenjie |
| contents | We present a projection-based, stability-preserving methodology for computing time correlation functions in open quantum systems governed by generalized quantum master equations with non-Markovian effects. Building upon the memory kernel coupling theory framework, our approach transforms the memory kernel hierarchy into a system of coupled linear differential equations through Mori-Zwanzig projection, followed by spectral projection onto stable eigenmodes to ensure numerical stability. By systematically eliminating unstable modes while preserving the physically relevant dynamics, our method guaranties long-time convergence without introducing artificial damping or ad hoc modifications. The theoretical framework maintains mathematical rigor through orthogonal projection operators and spectral decomposition. Benchmark calculations on the spin-boson model show excellent agreement with exact hierarchical equations of motion results while achieving significant computational efficiency. This approach provides a versatile and reliable framework for simulating non-Markovian dynamics in complex systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10629 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations Liu, Wei Bi, Rui-Hao Su, Yu Xu, Limin Zhou, Zhennan Wang, Yao Dou, Wenjie Quantum Physics Chemical Physics We present a projection-based, stability-preserving methodology for computing time correlation functions in open quantum systems governed by generalized quantum master equations with non-Markovian effects. Building upon the memory kernel coupling theory framework, our approach transforms the memory kernel hierarchy into a system of coupled linear differential equations through Mori-Zwanzig projection, followed by spectral projection onto stable eigenmodes to ensure numerical stability. By systematically eliminating unstable modes while preserving the physically relevant dynamics, our method guaranties long-time convergence without introducing artificial damping or ad hoc modifications. The theoretical framework maintains mathematical rigor through orthogonal projection operators and spectral decomposition. Benchmark calculations on the spin-boson model show excellent agreement with exact hierarchical equations of motion results while achieving significant computational efficiency. This approach provides a versatile and reliable framework for simulating non-Markovian dynamics in complex systems. |
| title | Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations |
| topic | Quantum Physics Chemical Physics |
| url | https://arxiv.org/abs/2602.10629 |