Quantum kinetic approach and the scattering approach to vacuum pair production

For Schwinger pair production with background electric fields varying only in time, it is shown that the quantum kinetic approach, based on the quantum Vlasov equation, and the quantum mechanical scattering approach are completely equivalent. This different perspective on the quantum kinetic approach suggests new approximation methods, which are tested in detail using a soluble pulselike field configuration, and may give useful insight for generalization to more general electric fields, varying in more than one dimension.

Figure 1

Quasiclassical regime, scalar case. Four approximation schemes are indicated. The plot shows the bell-shaped dependence of the pair production rate on $k_{\parallel }$, in units $m$. The field intensity is taken as $E=0.1E_{\mathrm{cr}}=0.1m^2$, and the field width is set to $\tau =10m$. The mass and charge are taken as 1. Normalized units ($\hslash =1$, $c=1$) were used for all numerical calculations.

Figure 2

The high intensity field regime, scalar case. Again, the bell-shaped dependence of the pair production rate on $k_{\parallel }$ is observed. Electric field intensity is taken as $E=0.8E_{\mathrm{cr}}=0.8m^2$. The field width is taken as $\tau =10m$. The mass and charge are taken as 1. It is observed that the rate changes drastically as the field intensity increases.

Figure 3

Quasiclassical regime for the spinor case. As in the scalar QED example in Fig. 1, we take $E=0.1E_{\mathrm{cr}}=0.1m^2$ and $\tau =10m$. The plot shows that the values for the pair production rate differ slightly from the scalar case.

Figure 4

High intensity field regime, spinor case. As in the scalar QED example in Fig. 2, we take $E=0.8E_{\mathrm{cr}}$ and $\tau =10m$.