Capacitor Discharge and Vacuum Resistance in Massless QED_2

TL;DR

This paper analyzes the quantum discharge of a capacitor in 1+1 dimensional massless QED, revealing oscillatory electric fields, vacuum conductivity, and connections to black hole evaporation.

Contribution

It provides a full quantum analysis of capacitor discharge including backreaction, and calculates the vacuum's electrical conductivity in massless QED.

Findings

Electric field oscillations decay as t^{-1/2}

Vacuum electrical conductivity is e/π^{1/2}

Stronger coupling slows the decay of oscillations

Abstract

A charged parallel plate capacitor will create particle-antiparticle pairs by the Schwinger process and discharge over time. We consider the full quantum discharge process in 1+1 dimensions including backreaction, when the electric field interacts with massless charged fermions. We recover oscillatory features in the electric field observed in a semiclassical analysis and find that the amplitude of the oscillations falls off as t^{-1/2} and that stronger coupling implies slower decay. Remarkably, Ohm's law applies to the vacuum and we evaluate the quantum electrical conductivity of the vacuum to be e/\pi^{1/2}, where e is the fermionic charge. Similarities and differences with black hole evaporation are mentioned.