Exact WKB analysis of the vacuum pair production by time-dependent electric fields

Abstract

We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis. We identify the generic structure of a Stokes graph for systems with the vacuum pair production and show that the number of produced pairs is given by a product of connection matrices for Stokes segments connecting pairs of turning points. We derive an explicit formula for the number of produced pairs, assuming the semi-classical limit. The obtained formula can be understood as a generalization of the divergent asymptotic series method by Berry, and is consistent with other semi-classical methods such as the worldline instanton method and the steepest descent evaluation of the Bogoliubov coefficients done by Brezin and Izykson. We also use the formula to discuss effects of time-dependence of the applied strong electric field including the interplay between the perturbative multi-photon pair production and non-peturbative Schwinger mechanism, and the dynamically assisted Schwinger mechanism.

Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S1

“…• Schwinger mechanism for time-dependent electric field [67], where the Klein-Gordon equation in scalar QED has a Schrödinger-equation form.…”

The exact WKB and the Landau-Zener transition for asymmetry in cosmological particle production

“…Besides the preheating scenario, there are many papers considering the famous Schwinger mechanisms in cosmology. The Schwinger mechanism [24], which is named after Schwinger who first derived the exponential formula for the pair production, is still an active research target [25][26][27]. We also suppose phase transition or decay of unstable domain wall networks for our scenario, which is also expected to cause similar particle production.…”

“…we have applied the EWKB to cosmological particle production (without asymmetry). Seerefs [27,[32][33][34]. for more references.…”

“…In this paper, we are using the EWKB for qualitative analysis 14. In terms of the EWKB, each MTP gives the transfer matrix similar to the scattering by an independent inverted quadratic potential, which is calculable[27,[32][33][34]. In this sense, each MTP is separable.…”

Chemical-potential-assisted particle production in FRW spacetimes

“…We note that there are many past studies in the literature that utilize the Stokes phenomenon to study particle production. For example, it is applied to the Sauter-Schwinger effect [38][39][40][41][42][43], to Hawking radiation [44], to the adiabatic particle number in global de Sitter (dS) spacetime [45][46][47], to dark matter production at the end of inflation [48], to preheating [49,50], and to particle production triggered by vacuum decay [51]. An excellent review is recently given in [52].…”