تقرير
Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
| العنوان: | Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems |
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| المؤلفون: | Hue, Jun Hao, Eren, Ege, Chiew, Shao Hen, Lau, Jonathan Wei Zhong, Chang, Leo, Chau, Thanh Tri, Trappe, Martin-Isbjörn, Englert, Berthold-Georg |
| سنة النشر: | 2020 |
| المجموعة: | Physics (Other) |
| مصطلحات موضوعية: | Physics - Computational Physics |
| الوصف: | 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. Comment: 14 pages, 6 figures; for accompanying open-source program, see https://github.com/huehou/Fourth-Order-Leapfrog |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2007.05308 |
| رقم الأكسشن: | edsarx.2007.05308 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |