Spatially Assisted Schwinger Mechanism and Magnetic Catalysis
  Using the worldline formalism we compute an effective action for fermions under a temporally modulated electric field and a spatially modulated magnetic field. It is known that the former leads to an enhanced Schwinger Mechanism, while we find that the latter can also result in enhanced particle production and even cause a reorganization of the vacuum to acquire a larger dynamical mass in equilibrium which spatially assists the Magnetic Catalysis. 
Patrick Copinger, Kenji Fukushima
hep-th hep-ph