%0 Journal Article
%T On the Vlasov equation for Schwinger pair production in a time-dependent electric field
%A Adolfo Huet
%A Sang Pyo Kim
%A Christian Schubert
%J Physics
%D 2014
%I arXiv
%R 10.1103/PhysRevD.90.125033
%X Schwinger pair creation in a purely time-dependent electric field can be described through a quantum Vlasov equation describing the time evolution of the single-particle momentum distribution function. This equation exists in two versions, both of which can be derived by a Bogoliubov transformation, but whose equivalence is not obvious. For the spinless case, we show here that the difference between these two evolution equations corresponds to the one between the "in-out" and "in-in" formalisms. We give a simple relation between the asymptotic distribution functions generated by the two Vlasov equations. As examples we discuss the Sauter and single-soliton field cases.
%U http://arxiv.org/abs/1411.3074v2