On the Vlasov equation for Schwinger pair production in a time-dependent electric field
arXiv:1411.3074 · doi:10.1103/PhysRevD.90.125033
Abstract
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.
15 pages, 2 figures, final published version (substantially extended)
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- Generalized Gelfand-Dikii equation for fermionic Schwinger pair production
- The physics of adiabatic particle number in the Schwinger effect
- Nonadiabatic quantum kinetic equations and Dirac-Heisenberg-Wigner formalism for Schwinger pair production in time-varying electric fields with multiple components
- When does the Schwinger Preheating Occur?