Finite-size effect in the Schwinger particle-production mechanism

Abstract

The Schwinger mechanism of particle production in a strong and uniform electric field for an infinite system is generalized to the case where the strong field is confined between two condenser plates separated by a finite distance. The production rates, for both bosons and fermions, are obtained by solving the Klein-Gordon equation and the Dirac equation in a linear vector potential. They are expressed in terms of parabolic cylinder functions for bosons, and in terms of the confluent hypergeometric functions for fermions. Numerical evaluation of these results shows large deviations of the production rate from what one deduces with the Schwinger formula, indicating a large finite-size effect in particle production.