经典和量子系统数值时间演化的四阶蛙跳算法
Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
摘要：
Chau等人[New J. Phys. 20，073003（2018）]提出了时间演化算子的四阶近似“$U_7$”的新的直接推导，并暗示了其作为辛积分器的潜在价值。$U_7$基于Suzuki-Trotter分裂算子方法，并导致一种优于现有方法的数值时间传播算法。我们基准性能的$U_7$和其他算法，包括龙格-库塔法和另一个最近开发的铃木-特罗特为基础的计划，这是确切的四阶演化参数，对各种经典和量子系统。我们发现$U_7$在这里测试的所有系统和算法中以最低的计算成本提供任何给定的目标精度。这项研究是伴随着开源的数值软件，我们希望将证明在课堂上有价值。
英文摘要：
Chau et al. [New J. Phys. 20, 073003 (2018)] presented a new and straight-forward derivation of a fourth-order approximation '$U_7$' of the time-evolution operator and hinted at its potential value as a symplectic integrator. $U_7$ is based on the Suzuki-Trotter split-operator method and leads to an algorithm for numerical time propagation that is superior to established methods. We benchmark the performance of $U_7$ and other algorithms, including a Runge-Kutta method and another recently developed Suzuki-Trotter-based scheme, that are exact up to fourth order in the evolution parameter, against various classical and quantum systems. We find $U_7$ to deliver any given target accuracy with the lowest computational cost, across all systems and algorithms tested here. This study is accompanied by open-source numerical software that we hope will prove valuable in the classroom.
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