Resonant particle creation by a time-dependent potential in a nonlocal theory

Considering an exactly solvable local quantum theory of a scalar field interacting with a $\delta$-shaped time-dependent potential we calculate the Bogoliubov coefficients analytically and determine the spectrum of created particles. We then show how these considerations, when suitably generalized to a specific nonlocal "infinite-derivative" quantum theory, are impacted by the presence of nonlocality. In this model, nonlocality leads to a significant resonant amplification of certain modes, leaving its imprint not only in the particle spectrum but also in the total number density of created particles.