Temperature of Electron Fluctuations in an Accelerated Vacuum

TL;DR

This paper investigates the temperature and spectral structure of electron vacuum fluctuations under constant acceleration and electric fields, revealing Boson-like and Fermi-like behaviors related to the Unruh effect.

Contribution

It demonstrates that vacuum fluctuations in a constant electric field exhibit Boson-like spectral density and temperature, connecting these findings to the Unruh temperature for classical particles.

Findings

Vacuum fluctuations have a Boson-like spectral density with temperature proportional to acceleration.

Classical particles show a Fermi-like structure with a temperature matching the Unruh temperature.

Vacuum fluctuations do not vanish under constant acceleration, indicating persistent quantum effects.

Abstract

The electron vacuum fluctuations measured by $\cond$ do not vanish in an externally applied electric field $\calE$. For an exactly constant field, that is for vacuum fluctuations in presence of a constant accelerating force, we show that $\cond$ has a Boson-like structure with spectral state density $\tanh^{-1}(E/m)$ and temperature $\TEH = e\calE/m\pi = a_v/\pi$. Considering the vacuum fluctuations of `classical' gyromagnetic ratio $g=1$ particles we find Fermi-like structure with the same spectral state density at a smaller temperature $T_1=a_v/2\pi$ which corresponds to the Unruh temperature of an accelerated observer.