AI 中文总结
本研究提出高性能开源强场量子动力学框架TDSE-Z，基于自适应B样条网格实现厄米算符弱形式离散，通过多类基准验证了求解精度与CPU强可扩展性，为跨尺度强场动力学研究及超算拓展提供模块化工具。
AI 中文摘要
我们提出了\textsc{TDSE-Z}，这是一款面向原子、分子与半导体有效质量体系强场量子动力学研究的高性能开源框架。其核心引擎在几何自适应B样条网格上实现了厄米BenDaniel-Duke算符$\tilde{T}_{\text{BDD}} = -\frac{1}{2}\nabla(m^{-1}(\boldsymbol{r})\nabla)$的弱形式伽辽金离散，支持1至3维下的任意势场与可定制激光构型。我们通过两项严格基准验证了静态位置相关质量（PDM）本征求解器：一是与解析Quesne PDM模型的对比，二是$\text{GaAs/Al}_{0.3}\text{Ga}_{0.7}\text{As}$双量子阱测试，计算得到的隧穿劈裂指数衰减特性与Wentzel-Kramers-Brillouin（WKB）理论符合度达亚百分比级别。我们进一步在恒定质量体系上验证了时间传播引擎，精准复现了原子基准中的高次谐波产生（HHG）谱，并证实了维度对于完整捕捉强光-物质相互作用的重要性。我们的实现展现出优异的强可扩展效率，在数百个CPU核心上仍能保持性能。目前静态本征求解器支持可选GPU卸载，时间传播引擎则针对CPU优化，其模块化架构为未来向百亿亿次级量子动力学拓展提供了基础。
英文摘要
We present \textsc{TDSE-Z}, a high-performance open-source framework for strong-field quantum dynamics in atomic, molecular, and semiconductor effective-mass systems. The core engine implements a weak-form Galerkin discretisation of the Hermitian BenDaniel-Duke operator, $\hat{T}_{\mathrm{BDD}} = -\frac{1}{2}\nabla\cdot(m^{-1}(\mathbf{r})\nabla)$, on geometry-adapted B-spline meshes, supporting arbitrary potentials and customisable laser configurations in one to three dimensions. We validate the static position-dependent-mass (PDM) eigensolver through two stringent benchmarks: a comparison to the analytical Quesne PDM model and a $\text{GaAs/Al}_{0.3}\text{Ga}_{0.7}\text{As}$ double quantum well, where the exponential decay of computed tunnel splittings follows Wentzel-Kramers-Brillouin (WKB) theory at the sub-percent level. We further demonstrate the time-propagation engine on constant-mass systems, accurately reproducing high-harmonic generation (HHG) spectra in atomic benchmarks and confirming the importance of dimensionality in fully capturing the strong light-matter interaction. Our implementation demonstrates robust strong-scaling efficiency, maintaining performance across hundreds of CPU cores. While the static eigensolver currently supports optional GPU offloading, the time-propagation engine is CPU-optimised, providing a modular architecture for future expansion toward exascale quantum dynamics.
