Particle creation in a time-dependent electric field revisited

TL;DR

This paper revisits particle creation in a time-dependent electric field using Gaussian state formalism, analyzing the evolution of particle content and comparing it with cosmological scenarios, revealing rapid saturation of particle production.

Contribution

It applies a Gaussian state formalism to analyze time-dependent particle creation in electric fields, including localized spikes, providing new insights into the dynamics of quantum fields.

Findings

Particle creation occurs over a short time interval.

Particle content saturates quickly after field activation.

Comparison with de Sitter space highlights similarities in power spectra.

Abstract

We adopt the general formalism for analyzing evolution of gaussian states of quantized fields in time-dependent backgrounds in the Schrodinger picture (presented in detail in arXiv:0708.1233 and 0708.1237) to study the example of a spatially uniform electric field background (in a time-dependent gauge) which is kept turned on for a finite duration of time. In particular, we study the \emph{time-dependent} particle content, defined in terms of the concept of instantaneous eigenstates, and describe how it captures the time evolution of the quantized field modes. The actual particle creation process occurs over a relatively short interval in time, and the particle content saturates rather quickly. We also compare the \emph{power spectrum} of the field modes, computed in the asymptotic limit, with the corresponding situation in a cosmological de Sitter background. Particle creation under the influence of a spiked electric field localized in time, as a particular limiting case of the above general model, is also considered.