论文标题
对于经典和量子系统的数值时间演变的四阶Leapfrog算法
Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
论文作者
论文摘要
Chau等。 [New J. Phys。 20，073003（2018）]提出了一个新的，直截了当的派生，该近似值是时间进化运算符的四阶“ $ u_7 $”，并暗示其作为符号集成符的潜在价值。 $ U_7 $基于Suzuki-Trotter Split-Operator方法，并导致用于数值时间传播的算法，该算法优于已建立的方法。我们基于$ u_7 $和其他算法的性能，包括runge-kutta方法和另一个最近开发的基于铃木 - 漫游器的方案，这些方案在Evolution参数中与各种经典和量子系统相比，它们在Evolution参数中的精确性最高。我们发现$ u_7 $在此处测试的所有系统和算法中，以最低的计算成本提供了任何给定的目标准确性。这项研究伴随着开源数值软件，我们希望在课堂上证明有价值。
Chau et al. [New J. Phys. 20, 073003 (2018)] presented a new and straight-forward derivation of a fourth-order approximation '$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.
