Pair production beyond the Schwinger formula in time-dependent electric fields

We investigate electron-positron pair production in pulse-shaped electric background fields using a non-Markovian quantum kinetic equation. We identify a pulse length range for subcritical fields still in the nonperturbative regime where the number of produced pairs significantly exceeds that of a naive expectation based on the Schwinger formula. From a conceptual viewpoint, we find a remarkable quantitative agreement between the (real time) quantum kinetic approach and the (imaginary time) effective action approach.

Figure 1

Logarithmic plot of the number density $n[e^{+}{e}^{-}]$ calculated for $E_0=0.1E_{\mathrm{cr}}$ as a function of the temporal width $\tau$ in units of $[2·{10}^{-5}{\mathrm{eV}}^{-1}]$. Dashed line: solution obtained for the non-Markovian equation (4) and within the effective action approach Eq. (18). Dotted line: solution obtained within the low-density approximation Eq. (10). Solid line: solution obtained in the instantaneous approximation Eq. (19).

Figure 2

Momentum space plot of the asymptotic distribution function $f^{\mathrm{nM}}(\overrightarrow{k},\infty )$ calculated for $E_0=0.1E_{\mathrm{cr}}$ and $\tau =2·{10}^{-5}{\mathrm{eV}}^{-1}\approx 10·t_{\mathrm{c}}$. It is an advantage of the quantum kinetic approach that the position and the width of the peak of the distribution function in momentum space can be calculated very precisely.

Figure 3

Logarithmic plot of the number density calculated for $\tau =2·{10}^{-5}{\mathrm{eV}}^{-1}\approx 10·t_{\mathrm{c}}$ as a function of the field strength $E_0$. Dashed line: solution obtained for the non-Markovian equation (4) and within the effective action approach Eq. (18). Dotted line: solution obtained within the low-density approximation Eq. (10). Solid line: solution obtained in the instantaneous approximation Eq. (20).