Particle creation from the vacuum by an exponentially decreasing   electric field
  We analyze the creation of fermions and bosons from the vacuum by the exponentially decreasing in time electric field in detail. In our calculations we use QED and follow in main the consideration of particle creation effect in a homogeneous electric field. To this end we find complete sets of exact solutions of the $d$-dimensional Dirac equation in the exponentially decreasing electric field and use them to calculate all the characteristics of the effect, in particular, the total number of created particles and the probability of a vacuum to remain a vacuum. It should be noted that the latter quantities were derived in the case under consideration for the first time. All possible asymptotic regimes are discussed in detail. In addition, switching on and switching off effects are studied. 
T.C. Adorno, S.P. Gavrilov, and D.M. Gitman
hep-th