Scattering and pair creation by a constant electric field between two capacitor plates

TL;DR

This paper investigates particle scattering and vacuum instability caused by a finite, constant electric field between capacitor plates, deriving formulas for particle creation and showing thermal similarities to black hole radiation.

Contribution

It introduces exact solutions and asymptotic formulas for particle creation in a finite electric field, extending previous quantum field theory analyses to the L-constant electric field scenario.

Findings

Derived formulas for particle scattering probabilities.

Established asymptotic expressions for particle creation rates.

Showed thermal distribution similarity with black hole radiation.

Abstract

Using the quantum field theory approach developed in Phys. Rev. D. 93, 045002 (2016), we consider particle scattering and vacuum instability in the so-called L-constant electric field, which is a constant electric field confined between two capacitor plates separated by a finite distance L. We obtain and analyze special sets of stationary solutions of the Dirac and Klein-Gordon equations with the L-constant electric field. Then, we represent probabilities of particle scattering and characteristics of the vacuum instability (related to pair creation) in terms of the introduced solutions. From exact formulas, we derive asymptotic expressions for the differential mean numbers, for the total mean number of created particles, and for the vacuum-to-vacuum transition probability. Using the equivalence principle, we demonstrate that the distributions of particles created by the L-constant electric field and the gravitational field of a black hole have a similar thermal structure.