Papers › Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
Fourth-order leapfrog algorithms for numerical time evolution of classical and quantum systems
Jun Hao Hue, Ege Eren, Shao Hen Chiew, Jonathan Wei Zhong Lau, Leo Chang, Thanh Tri Chau, Martin-Isbjörn Trappe, Berthold-Georg Englert
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Chau et al. [New J. Phys. 20, 073003 (2018)] presented a new and straight-forward derivation of a fourth-order approximation 'U₇' of the time-evolution operator and hinted at its potential value as a symplectic integrator. U₇ 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 U₇ 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 U₇ 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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