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.

Figure 1

Pair production rate with the dynamically assisting $E$ with frequency $\omega$ and the spatially assisting $B$ with wave number $\kappa$ in units of the particle mass $m$, where we chose $eE=eB={10}^{-2}{m}^2$.

Figure 2

The same as Fig. 1, where we chose $eE=eB=m^2$.