AI 中文总结
研究含时哈密顿量下状态演化的克雷洛夫扩展复杂度，利用弗洛凯理论及马格努斯展开，包括全局和分段展开，为分析含时量子系统复杂度增长提供实用工具。
AI 中文摘要
我们研究了含时哈密顿量作用下状态演化的克雷洛夫扩展复杂度。对于周期性驱动系统，我们在弗洛凯理论框架内阐述问题，并展示了在弗洛凯哈密顿量没有闭式解时，马格努斯展开如何提供系统近似。我们将此框架扩展到非周期性驱动情况，证明除了全局截断马格努斯展开外，分段马格努斯展开在全局展开失去收敛性或精度时提供了可靠方法。我们的结果为分析一大类含时量子系统中的复杂度增长提供了实用工具。
英文摘要
We investigate Krylov spread complexity for states evolving under time-dependent Hamiltonians. For periodically driven systems, we formulate the problem within Floquet theory and show how the Magnus expansion provides a systematic approximation when the Floquet Hamiltonian is not available in closed form. We then extend this framework beyond periodic driving and demonstrate that, in addition to the globally truncated Magnus expansion, a piecewise Magnus expansion provides a reliable method when the global expansion loses convergence or accuracy. Our results provide practical tools for analyzing complexity growth in a broad class of time-dependent quantum systems.
Comments27 pages, 4 figures, Refs. updated
