Schwinger pairs production in a soft-wall model
  The Schwinger pairs production rate is calculated numerically in the soft-wall model with the help of a simpler method in determining the soft-wall's position beyond which probe strings connecting the Schwinger pairs do not fall into. Behaviours of the production rate in both the upper critical region and the middle linear part are studied carefully. The latter exhibits interesting new features un-noted previously. All results are presented in comparisons with hard-wall models. 
Feng Qu and Ding-fang Zeng
hep-th