  The non-equilibrium dynamics beyond linear response of Weyl semimetals is
studied after a sudden switching on of a DC electric field. The resulting
current is a nonmonotonic function of time, with an initial quick increase of
polarization current followed by a power-law decay. Particle-hole creation \`a
la Schwinger dominates for long times when the conduction current takes over
the leading role, with the total current increasing again. The conductivity
estimated from a dynamical calculation within a Drude picture agrees with the
one obtained from Kubo's formula. The full distribution function of
electron-hole pairs changes from Poissonian for short perturbations to a
Gaussian in the long perturbation (Landau-Zener) regime. The vacuum persistence
probability of high energy physics manifests itself in a finite probability of
no pair creation and no induced current at all times.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Quantum Gases