Particle Self-Bunching in the Schwinger Effect in Spacetime-Dependent Electric Fields

Nonperturbative electron-positron pair creation (the Schwinger effect) is studied based on the Dirac-Heisenberg-Wigner formalism in $1+1$ dimensions. An ab initio calculation of the Schwinger effect in the presence of a simple space- and time-dependent electric field pulse is performed for the first time, allowing for the calculation of the time evolution of observable quantities such as the charge density, the particle number density or the total number of created particles. We predict a new self-bunching effect of charges in phase space due to the spatial and temporal structure of the pulse.

Figure 1

Comparison of $\overline{n}(p,t\to \infty )$ for the full solution (solid) with the l.o. derivative expansion (dashed) and the local density approximation (dotted) for $\tau =10/m$, $E_0=0.5E_{\mathrm{cr}}$.

Figure 2

Comparison of $\overline{n}(p,t\to \infty )$ for $\tau =10/m$, $E_0=0.5E_{\mathrm{cr}}$ and different values of $\lambda$. Note that $\overline{n}(p,t\to \infty )=0$ for $\lambda ={\lambda }_C$.

Figure 3

Comparison of $\overline{N}(t\to \infty )$ for the full solution (solid) with the l.o. derivative expansion (dashed) and the local density approximation (dotted) for $\tau =10/m$, $E_0=0.5E_{\mathrm{cr}}$.