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arXiv · 1411.3074

On the Vlasov equation for Schwinger pair production in a time-dependent electric field

Adolfo Huet·Sang Pyo Kim·Christian Schubert
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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.

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Adolfo Huet, Sang Pyo Kim, Christian Schubert. 2015-01-26. On the Vlasov equation for Schwinger pair production in a time-dependent electric field. https://doi.org/10.1103/physrevd.90.125033

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