The Stochastic Schwinger Effect

TL;DR

The paper develops a stochastic generalisation of the Schwinger effect by treating the background gauge field as a Gaussian stochastic process and computing the vacuum decay rate and particle densities through the one-loop effective action. It provides closed-form analytic expressions for both scalar and fermionic productions in stationary and non-stationary backgrounds, using the proper-time representation and short-time Fourier analysis, in flat spacetime and at zero temperature. The authors illustrate the framework with phenomenological examples relevant to astrophysical plasmas, dark-photon backgrounds, and axion–gauge field reheating, showing that the stochastic channel can dominate or significantly modify conventional static-Schwinger or Breit–Wheeler processes depending on the regime. The work highlights how realistic, transient, and stochastic gauge-field configurations can trigger vacuum decay, offering insight into particle production during reheating and in extreme astrophysical environments, while outlining natural extensions to expanding backgrounds and backreaction effects for future study.

Abstract

We formulate a stochastic generalisation of the Schwinger effect, extending pair production to statistically fluctuating gauge-field backgrounds. Our approach captures realistic field configurations that are transient, inhomogeneous, and stochastic, as commonly encountered in cosmological and high-energy astrophysical settings. Using the effective action formalism, we compute the vacuum decay rate and number density of charged particles, obtaining closed-form analytical expressions for both scalar and fermionic cases. To isolate the essential physics, the analysis is performed in flat spacetime and at zero temperature, providing a controlled setting in which curvature and thermal effects can be neglected. As a proof of concept, we present representative phenomenological examples relevant to astrophysical plasmas and early-Universe-motivated scenarios.

Figures (2)

• Figure 1: Illustration of the short-time Fourier transform (STFT) with Gaussian windows. The orchid curve is the signal, the dashed orange curve the Gaussian window function, and the solid black curve the resulting windowed signal. The left panel shows the case $\sigma \gg 1$, where the wide Gaussian window leaves the sinusoidal signal essentially unchanged, corresponding to the global Fourier transform. The right panel shows a finite-width Gaussian window ($\sigma \approx 1/\Delta t$), which localises the analysis in time and demonstrates how the STFT resolves transient features.
• Figure 2: Comparison of the exact integrand (solid lines) with the analytical approximation (dashed lines) for different values of $z$ and $\xi$. Note that both integrands are defined over the domain $y \in [\sqrt{1+z^{-2}},\,\infty)$. The left panel shows the bosonic integrand in \ref{['eq:app-fbb']}, while the right panel shows the fermionic integrand in \ref{['eq:app-f-f']} in the right panels. The proposed approximation reproduces the exact integrand with excellent accuracy across different choices of $z$ and $\xi$ successfully capturing both the near-threshold behaviour and the peak structure. The quality of the fit improves with increasing $z$, precisely in the region that dominates the contribution to the resulting integral.