In this paper, we present an approach to deal with the dynamics of the Dirac equation with time-dependent electromagnetic potentials using the fourth-order compact time-splitting method ($S_\text{4c}$). To this purpose, the time-ordering technique for time-dependent Hamiltonians is introduced, so that the influence of the time-dependence could be limited to certain steps which are easy to treat. Actually, in the case of the Dirac equation, it turns out that only those steps involving potentials need to be amended, and the scheme remains efficient, accurate, as well as easy to implement. Numerical examples in 1D and 2D are given to validate the scheme.

中文翻译：

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时变势狄拉克方程的四阶紧致时间分裂方法

在本文中，我们提出了一种使用四阶紧凑时间分裂方法 ($S_\text{4c}$) 处理具有时间相关电磁势的狄拉克方程动力学的方法。为此，引入了时间相关哈密顿量的时间排序技术，以便将时间相关性的影响限制在某些易于处理的步骤中。实际上，在狄拉克方程的情况下，结果证明只需要修改涉及势能的那些步骤，并且该方案仍然有效、准确且易于实现。给出了一维和二维的数值例子来验证该方案。