Thermally versus dynamically assisted Schwinger pair production

We study electron-positron pair production by the combination of a strong, constant electric field and a thermal background. We show that this process is similar to dynamically assisted Schwinger pair production, where the strong field is instead assisted by another coherent field, which is weaker but faster. We treat the interaction with the photons from the thermal background perturbatively, while the interaction with the electric field is nonperturbative (i.e. a Furry picture expansion in $\alpha$). At $\mathcal{O}(\alpha^2)$ we have ordinary perturbative Breit-Wheeler pair production assisted nonperturbatively by the electric field. Already at this order we recover the same exponential part of the probability as previous studies, which did not expand in $\alpha$. This means that we do not have to consider higher orders, so our approach allows us to calculate the pre-exponential part of the probability, which has not been obtained before in this regime. Although the prefactor is in general subdominant compared to the exponential part, in this case it can be important because it scales as $\alpha^2\ll1$ and is therefore much smaller than the prefactor at $\mathcal{O}(\alpha^0)$ (pure Schwinger pair production). We show that, because of the exponential enhancement, $\mathcal{O}(\alpha^2)$ still gives the dominant contribution for temperatures above a certain threshold, but, because of the small prefactor, the threshold is higher than what the exponential alone would suggest.