驱动量子系统的高阶无交换子指数时间传播
High-order commutator-free exponential time-propagation of driven quantum systems
AI总结：
本文利用无交换子时间传播子求解含时薛定谔方程，通过哈密顿量加权和的指数乘积实现高阶、保幺正的时间传播，并提供了高达八阶的优化传播子及误差分析。
摘要：
我们讨论了使用无交换子时间传播子对含时哈密顿算符的薛定谔方程进行数值求解。这些传播子被构造为哈密顿算符简单加权和的指数乘积。由于其指数形式，它们严格保持了时间传播的幺正性。无交换子或其他计算复杂操作使得该方法易于实现，并适用于大规模稀疏矩阵问题。我们在Magnus展开的背景下解释了无交换子指数时间传播子的推导，并提供了高达八阶的优化传播子。给出了广泛的理论误差分析以及针对不同问题的实际效率测试。讨论了实际实现中的问题，特别是使用Krylov技术计算指数。我们通过两个高级示例——电场中的氢原子和泵浦的多相互作用二能级系统或自旋系统——证明了该方法能够实现快速准确的计算。
英文摘要：
We discuss the numerical solution of the Schrödinger equation with a time-dependent Hamilton operator using commutator-free time-propagators. These propagators are constructed as products of exponentials of simple weighted sums of the Hamilton operator. Owing to their exponential form they strictly preserve the unitarity of time-propagation. The absence of commutators or other computationally involved operations allows for straightforward implementation and application also to large scale and sparse matrix problems. We explain the derivation of commutator-free exponential time-propagators in the context of the Magnus expansion, and provide optimized propagators up to order eight. An extensive theoretical error analysis is presented together with practical efficiency tests for different problems. Issues of practical implementation, in particular the use of the Krylov technique for the calculation of exponentials, are discussed. We demonstrate for two advanced examples, the hydrogen atom in an electric field and pumped systems of multiple interacting two-level systems or spins that this approach enables fast and accurate computations.
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