Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fourth-order leapfrog algorithms for numerical time evolution of
  classical and quantum systems   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.

15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
5
The categories of this paper are: gr-qc
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex