# Spin-dependent dynamically assisted Schwinger mechanism

## TL;DR

This paper develops an analytical approach to the dynamically assisted Schwinger mechanism, revealing spin dependence and oscillatory behaviors in pair production under combined electric fields.

## Contribution

It derives an analytical formula for pair production numbers and uncovers spin dependence and oscillations related to the perturbation's frequency and angle.

## Key findings

- Analytical formula matches numerical results for weak/fast perturbations.
- Spin dependence emerges when the perturbation has a transverse component.
- Spin imbalance oscillates with perturbation frequency, angle, and particle momentum.

## Abstract

We study electron and positron pair production from the vacuum by a strong slow electric field superimposed by a weak fast electric field pointing in an arbitrary direction as a perturbation (the dynamically assisted Schwinger mechanism). An analytical formula for the production number is derived on the basis of the perturbation theory in the Furry picture. The formula is found to be in good agreement with non-perturbative results obtained by numerically solving the Dirac equation if the perturbation is sufficiently weak and/or is not very slow. We also find analytically/numerically that the Schwinger mechanism becomes spin-dependent if the perturbation has a transverse component with respect to the strong electric field. The number difference between spin up and down particles is strongly suppressed by an exponential of the critical field strength if the frequency of the perturbation is small, while it is only weakly suppressed by powers of the critical field strength if the frequency is large enough. We also find that the spin-imbalance exhibits non-trivial oscillating behaviors in terms of the frequency of the perturbation, the azimuthal angle, and the momentum of produced particles.