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.
Highlights
In 1931 [4], the vacuum pair production has been under intensive investigation as a fundamental prediction of quantum-field theory and to understand actual physics processes under extreme conditions as well as some analogous phenomena with different kinds of fields/forces
We study the vacuum pair production by a time-dependent strong electric field based on the exact WKB analysis
We have studied the vacuum pair production by a time-dependent strong electric field on the basis of the exact WKB analysis under the semi-classical approximation
Summary
To be self-contained, we here review the basics of the exact WKB analysis. The exact. Note that Berry [75] assumes some truncation of the series (2.8) and only considers the leading order factorial divergence of ψ± to compute (a correspondence of) the Borel transformation (2.9), and further employs the saddle point method to evaluate the Borel sum (2.10) Such treatments are unneeded in the exact WKB analysis. Let us consider two Borel sums, say Φ±,I and Φ±,II, defined on two neighboring Stokes regions, I and II, separated by a Stokes line Czt. For an analytic potential Q having the property (2.12), one can explicitly evaluate the discontinuity by carrying out the integration around the.
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