Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production

Details Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production

2011-10-05

arxiv.org/abs/1110.0900v2

Physical Review D 84, 125028 (2011)

Physics

High Energy Physics

High Energy Physics - Theory

5 pages, final published version, minor modifications

Scientific paper

10.1103/PhysRevD.84.125028

Using Lewis-Riesenfeld theory, we derive an exact non-adiabatic master equation describing the time evolution of the QED Schwinger pair production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov type integral equation, or as a third-order differential equation. In the last version it relates to the KdV equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of time-like delta function pulse fields is also shortly considered. We compare with previous approaches to the purely time-dependent field case.

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