Entropy of Schwinger pair production in time-dependent Sauter pulse electric field

TL;DR

This paper explores various entropy measures in electron-positron pair production under a time-dependent Sauter pulse electric field, revealing their relationships and behaviors for different pulse durations and momentum considerations.

Contribution

It introduces a comprehensive analysis of multiple entropy types in pair production, including entanglement and thermal entropies, and examines their behaviors in short and long pulse regimes with full momentum consideration.

Findings

Entanglement entropy is higher than thermal entropy for short pulses.

Chemical potential induces non-monotonic behavior in thermal entropy.

Both entropies saturate asymptotically, with thermal entropy reaching a higher value.

Abstract

We investigate entropy of electron-positron pair production in time-dependent Sauter pulse electric field. Both cases of pair longitudinal momentum only and full momentum consideration are examined. We further examine three types of entropy, one is the usual entanglement entropy $S_{\text{E}}$, the other two extensions are thermal distribution entropy $S_{\text{Th}}$, and that with the chemical potential correction, $S_{\text{Th,CP}}$. For short pulse, $S_{\text{E}}$ is higher than $S_{\text{Th}}$ and vice versa for long pulse. The chemical potential causes the single-particle average thermal distribution entropy $\frac{S_{\text{Th,CP}}}{N}$ to exhibit non-monotonic behavior, similar to the single-particle average entanglement entropy $\frac{S_{\text{E}}}{N}$ in the short-pulse range. In the full momentum case, we calculate the thermal distribution entropy $S_{\text{Th, U}}$ via introducing the Unruh temperature as the local effective temperature. We find that both $S_{\text{Th, U}}$ and $S_{\text{E}}$ saturate asymptotically to the constant while the former has a larger asymptotic value. The results presented in this study reveals that the different entropies have some delicate relationships among them.