Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
Abstract
Chau et al. [New J. Phys. 20, 073003 (2018)] presented a new and straight-forward derivation of a fourth-order approximation '' of the time-evolution operator and hinted at its potential value as a symplectic integrator. 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 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 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.
Cite
@article{arxiv.2007.05308,
title = {Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems},
author = {Jun Hao Hue and Ege Eren and Shao Hen Chiew and Jonathan Wei Zhong Lau and Leo Chang and Thanh Tri Chau and Martin-Isbjörn Trappe and Berthold-Georg Englert},
journal= {arXiv preprint arXiv:2007.05308},
year = {2020}
}
Comments
14 pages, 6 figures; for accompanying open-source program, see https://github.com/huehou/Fourth-Order-Leapfrog