Simulating fermion production in 1+1 dimensional QED

We investigate fermion-antifermion production in 1 + 1 dimensional QED using real-time lattice techniques. In this nonperturbative approach the full quantum dynamics of fermions is included, while the gauge field dynamics can be accurately represented by classical-statistical simulations for relevant field strengths. We compute the nonequilibrium time evolution of gauge-invariant correlation functions, implementing low-cost Wilson fermions. Introducing a lattice generalization of the Dirac-Heisenberg-Wigner function, we recover the Schwinger formula in 1 + 1 dimensions in the limit of a static background field. We discuss the decay of the field due to the backreaction of the created fermion-antifermion pairs and apply the approach to strongly inhomogeneous gauge fields. The latter allows us to discuss the striking phenomenon of a linear rising potential building up between produced fermion bunches after the initial electric pulse ceased.