Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production

TL;DR

This paper derives an exact non-adiabatic quantum Vlasov equation for Schwinger pair production in time-varying electric fields, enabling precise analysis of pair creation dynamics with novel mathematical connections.

Contribution

It introduces a new exact non-adiabatic master equation for Schwinger pair production, linking it to the KdV equation and providing exact solutions for general time-dependent fields.

Findings

Derived an exact non-adiabatic master equation for pair production.

Connected the equation to the KdV soliton solutions.

Compared new approach with previous methods for time-dependent fields.

Abstract

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.