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

Understand

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.