基于隐式常微分方程的3+1维Heisenberg-Euler方程数值解
An implicit ODE-based numerical solver for the simulation of the Heisenberg-Euler equations in 3+1 dimensions
摘要：
随着超高功率激光器的出现，量子电动力学（QED）真空的非线性性质得以探索。由于基础方程的高度非线性结构，需要新的数值算法。本文导出了一个数值模拟三维加时间的QED真空非线性光学效应的方法。讨论了它的性质。借助已知的分析结果验证了数值方法的有效性。该算法用于探索非线性真空的非线性全光学效应，解析方法是低效的或不可能的。
英文摘要：
With the advent of ultra-high power lasers the nonlinear nature of the vacuum of quantum electrodynamics (QED) can be probed. Due to the highly nonlinear structure of the underlying equations new numerical algorithms are required. A numerical scheme for simulating the nonlinear optical effects of the QED vacuum in up to 3 spatial dimensions plus time is derived. Its properties are discussed. The validity of the numerical approach is verified with the help of known analytic results. The algorithm is used to explore nonlinear all optical effects of the nonlinear vacuum for which analytic methods are inefficient or impossible.
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