Heisenberg-Euler弱场展开中非线性量子真空的数值模拟
Numerical Simulations of the Nonlinear Quantum Vacuum in the Heisenberg-Euler Weak-Field Expansion
AI总结：
本文提出求解Heisenberg-Euler弱场展开领头阶非线性方程的高精度数值格式，并用解析结果及二维、三维谐波产生场景验证其模拟量子真空效应的能力。
摘要：
量子真空的Heisenberg-Euler理论以非线性光-光相互作用补充了Maxwell电磁理论。这些相互作用源于真空涨落——量子理论的一项关键预言，并可由高强度激光脉冲触发，从而引起多种引人入胜的现象。本文提出了一种高精度数值格式，用于求解由Heisenberg-Euler弱场展开的领头阶所产生的非线性方程。该算法即使在相当小的波长下也具有近似线性的真空色散关系，并纳入了非物理模滤波器。所实现的求解器在一个空间维度上针对真空双折射和谐波产生的一系列已知解析结果进行了测试。文中还在两个和三个空间维度中演示了更复杂的谐波产生场景。
英文摘要：
The Heisenberg-Euler theory of the quantum vacuum supplements Maxwell's theory of electromagnetism with nonlinear light-light interactions. These originate in vacuum fluctuations, a key prediction of quantum theory, and can be triggered by high-intensity laser pulses, causing a variety of intriguing phenomena. A highly accurate numerical scheme for solving the nonlinear equations due to the leading orders of the Heisenberg-Euler weak-field expansion is presented. The algorithm possesses an almost linear vacuum dispersion relation even for comparably small wavelengths and incorporates a nonphysical modes filter. The implemented solver is tested in one spatial dimension against a set of known analytical results for vacuum birefringence and harmonic generation. More complex scenarios for harmonic generation are demonstrated in two and three spatial dimensions.
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