Schwinger pair production at nonzero temperatures or in compact directions

Adam R Brown

doi:10.1103/physrevd.98.036008

Abstract

Electric fields may decay by quantum tunneling: as calculated by Schwinger, an electron-positron pair may be summoned from the vacuum. In this paper I calculate the pair-production rate at nonzero temperatures. I find that at high temperatures the decay rate is dominated by a new instanton that involves both thermal fluctuation and quantum tunneling; this decay is exponentially faster than the rate in the literature. I also calculate the decay rate when the electric field wraps a compact circle (at zero temperature). The same new instanton also governs this rate: I find that for small circles decay is dominated by a process that drops the electric field by one unit, but does not produce charged particles.

Highlights

A uniform electric field is classically stable but quantum mechanically unstable
The dominant decay channel is the nucleation of an electronpositron pair, which discharges a single unit of flux
Barriers that may be traversed by quantum tunneling may be traversed by thermal fluctuation

Summary

INTRODUCTION

A uniform electric field is classically stable but quantum mechanically unstable. In the semiclassical regime, the dominant decay channel is the nucleation of an electronpositron pair, which discharges a single unit of flux. I will show that at high temperature (T > Tc ≡ ħ e2jmE⃗ j) the electric field decays by a process in which the electron-positron pair first thermally fluctuates partway up the barrier to nucleation, and only quantum tunnels through the rest. For L < Lc this is exponentially faster than the Schwinger process: decay rateL

WKB METHOD

DISCUSSION