量子系统与经典场相互作用保结构几何模拟算法关键技术开发与应用研究

With the fast development of ultra-short pulsed strong laser, high-power microwave, and steady-state strong field techniques, the new disciplines such as high energy density physics, experimental astrophysics, accelerator physics, and modern controlled fusion technologies are experiencing a rapid rise and merging. In these categories, the interaction between strong electromagnetic field and quantum system in plasmas as a core problem exceeds time-dependent perturbative theory, across direct ionization threshold, closes to relativistic limit, and moves into non-linear quantum electrodynamics interval. The strong-field matter states are very complex, where the plasma consists of atoms, molecules, ions, electrons, and photons shows extremely non-linear effects. Then accurate, efficient, and robust non-perturbative methods are needed. This project starts from a self-consistent field model. The Schrödinger-Maxwell equations are used to describe classical electromagnetic field interacts with non-relativistic quantum systems. The Dirac-Maxwell equations are used to describe classical electromagnetic field interacts with relativistic quantum systems. Based on the analysis of configuration and phase spaces geometric structures of physics models, canonical symplectic, non-canonical symplectic, and discrete differential geometric techniques are used to construct universal structure-preserving geometric simulation algorithms on relevant manifolds. Then a first-principle based quantum-system classical-field interaction physics simulation framework can be obtained. The algorithms will be tested by standard single-electron strong-field physics problems. The simulation framework will be used to do long-term multi-scale simulations of a class of frontier problems, such as strong-field ionization, quantum chaos, and nano-cavity quantum electrodynamics etc. This project could provide us with an ab initio simulation capability for quantum-system classical-field interactions with long-term accuracy and fidelity.

随着超短脉冲强激光、高功率微波与稳态强场技术的发展,高能量密度物理、实验天体物理、加速器物理与现代受控核聚变等学科迅速崛起并交融。其中处于核心地位的强电磁场与等离子体中的量子系统相互作用问题超越了含时微扰论,跨越了直接电离阈,已逼近相对论极限。量子系统-经典场相互作用问题表现出复杂的多尺度非线性效应,需要精确、高效、稳定的非微扰处理方法。本课题从自洽场模型出发,用Schrödinger-Maxwell系统描述经典电磁场与非相对论性量子系统相互作用,用Dirac-Maxwell系统描述经典电磁场与相对论性量子系统相互作用,分析物理模型的动力学几何结构,在相应流形上通过正则辛、非正则辛和离散微分几何技术构造保结构几何模拟算法,建立适用于量子系统-经典场相互作用问题的第一性原理计算框架。用量子力学标准问题检验算法。对强场电离、量子混沌、纳米腔量子电动力学等前沿问题进行大规模多尺度数值模拟研究。

以强电磁场与等离子体中的量子系统相互作用现象为核心的极端条件下的辐射与物质相互作用问题在强场物理、高能量密度物理、天体物理、加速器物理与现代受控核聚变等学科及相关交叉领域中占据了主导地位。为精确地处理其中的非线性多尺度效应，更好地研究其中蕴含的复杂物理，需要发展精确、高效、稳定的非微扰数值模拟方法。本项目围绕量子系统与经典场相互作用问题开展了一系列原创性研究，取得的主要研究进展包括建立了自洽的相对论性量子电动力学半离散格点场论，构造了一系列针对经典半离散格点场论的高阶保结构几何模拟算法，设计了极端强场条件下的非平衡态量子场模拟方案，在国产异构高性能计算平台上优化定型了强场量子电动力学保结构实时格点场论程序，实现了非线性Schwinger效应和真空Kerr效应等极端强场问题的高质量数值模拟研究，在纳米等离激元光子学和聚变等离子体物理等交叉方向发展了一系列保结构几何模拟算法并在相关方向成功实现了大量的数值实验。在本项目的支持下，课题组共发表物理学主流期刊论文10篇和国际会议论文1篇，项目研究成果对推进高能量密度物理及相关学科的理论和数值模拟研究有积极意义。

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