Role of switching-on and -off effects in the vacuum instability

TL;DR

This paper derives exact formulas for particle creation in a finite-duration electric field with switching effects, analyzing how rapid switching influences vacuum instability beyond slow variation approximations.

Contribution

It provides exact solutions for vacuum particle production in a composite electric field with switching effects, extending understanding beyond slow variation approximations.

Findings

Exact differential mean numbers for fermions and bosons are obtained.

Switching effects significantly influence particle creation when the field varies rapidly.

The locally constant field approximation is valid for slowly varying fields.

Abstract

We find exact differential mean numbers of fermions and bosons created from the vacuum due to a composite electric field of special configuration. This configuration imitates a finite switching-on and -off regime and consists of fields that switch-on exponentially from the infinitely remote past, remains constant during a certain interval $T$ and switch-off exponentially to the infinitely remote future. We show that calculations in the slowly varying field approximation are completely predictable in the framework of a locally constant field approximation. Beyond the slowly varying field approximation, we study effects of fast switching-on and -off in a number of cases when the size of the dimensionless parameter $\sqrt{eE}T$ is either close or exceeds the threshold value that determines the transition from a regime sensitive to on-off parameters to the slowly varying regime for which these effects are secondary.