Quantum Electrodynamics vacuum polarization solver
  The self-consistent modeling of vacuum polarization due to virtual electron-positron fluctuations is of relevance for many near term experiments associated with high intensity radiation sources and represents a milestone in describing scenarios of extreme energy density. We present a generalized finite-difference time-domain solver that can incorporate the modifications to Maxwell's equations due to vacuum polarization. Our multidimensional solver reproduced in one-dimensional configurations the results for which an analytic treatment is possible, yielding vacuum harmonic generation and birefringence. The solver has also been tested for two-dimensional scenarios where finite laser beam spot sizes must be taken into account. We employ this solver to explore different types of laser configurations that can be relevant for future planned experiments aiming to detect quantum vacuum dynamics at ultra-high electromagnetic field intensities. 
Thomas Grismayer, Rui Torres, Pedro Carneiro, F\`abio Cruz, Ricardo   Fonseca, Lu\'is O. Silva
physics.plasm-ph hep-th physics.comp-ph