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arXiv · 2602.10629

Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations

Wei Liu·Rui-Hao Bi·Yu Su·Limin Xu·Zhennan Zhou·Yao Wang·Wenjie Dou
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Abstract

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.

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Wei Liu, Rui-Hao Bi, Yu Su, Limin Xu, Zhennan Zhou, Yao Wang, Wenjie Dou. 2026-02-11. Projection-Based Memory Kernel Coupling Theory for Quantum Dynamics: A Stable Framework for Non-Markovian Simulations. https://arxiv.org/abs/2602.10629

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