Al-Naseri Haidar, Zamanian Jens, Brodin Gert
Department of Physics, Umeå University, SE-901 87 Umeå, Sweden.
Phys Rev E. 2021 Jul;104(1-2):015207. doi: 10.1103/PhysRevE.104.015207.
We derive a system of coupled partial differential equations for the equal-time Wigner function in an arbitrary strong electromagnetic field using the Dirac-Heisenberg-Wigner formalism. In the electrostatic limit, we present a system of four coupled partial differential equations, which are completed by Ampères law. This electrostatic system is further studied for two different cases. In the first case, we consider linearized wave propagation in a plasma accounting for the nonzero vacuum expectation values. We then derive the dispersion relation and compare it with well-known limiting cases. In the second case, we consider Schwinger pair production using the local density approximation to allow for analytical treatment. The dependence of the pair production rate on the perpendicular momentum is investigated and it turns out that the spread of the produced pairs along with perpendicular momentum depends on the strength of the applied electric field.
我们使用狄拉克 - 海森堡 - 维格纳形式体系，推导出了任意强电磁场中等时维格纳函数的耦合偏微分方程组。在静电极限情况下，我们给出了一个由四个耦合偏微分方程组成的系统，该系统由安培定律补充完整。针对两种不同情况对这个静电系统进行了进一步研究。在第一种情况下，我们考虑了等离子体中考虑非零真空期望值的线性化波传播。然后我们推导出色散关系，并将其与著名的极限情况进行比较。在第二种情况下，我们使用局部密度近似来考虑施温格对产生，以便进行解析处理。研究了对产生率对垂直动量的依赖性，结果表明产生的对沿垂直动量的展宽取决于所施加电场的强度。
