Quantum tunnelling from vacuum in multidimensions

TL;DR

This paper investigates quantum vacuum tunnelling in multidimensional electric fields, analyzing how spatial and temporal inhomogeneities influence pair production rates using worldline instantons and geometric methods.

Contribution

It introduces a novel analytical approach to estimate tunnelling thresholds and compute pair production in complex, multidimensional electric backgrounds with various temporal profiles.

Findings

Large dynamical enhancement of pair production rates.

Distinct effects of analytic structure on tunnelling in composite backgrounds.

Significant differences caused by temporal variations of Sauter-type fields.

Abstract

The tunnelling of virtual matter-antimatter pairs from the quantum vacuum in multidimensions is studied. We consider electric backgrounds as a linear combination of a spatial Sauter field and, interchangeably, certain weaker time dependent fields without poles in the complex plane such as the sinusoidal and Gaussian cases. Based on recent geometric considerations within the worldline formalism, we employ the relevant critical points in order to analytically estimate a characteristic threshold for the temporal inhomogeneity. We set appropriate initial conditions and apply additional symmetry constraints in order to determine the classical periodic paths in spacetime. Using these worldline instantons, we compute the corresponding leading order exponential factors showing large dynamical enhancement in general. We work out the main differences caused by the analytic structure of such composite backgrounds and also discuss the case with a strong temporal variation of Sauter-type.