Multidimensional quantum tunneling in the Schwinger effect

Abstract

We study the Schwinger effect, in which the external field having a spatiotemporal profile creates electron-positron pairs via multidimensional quantum tunneling. Our treatment is based on the trace formula for the QED effective action, whose imaginary part is represented by a sum over complex worldline solutions. The worldlines are multiperiodic, and the periods of motion collectively depend on the strength of spatial and temporal inhomogeneity. We argue that the classical action that leads to the correct tunneling amplitude must take into account both the full period, $\tilde{T}$ and the first fundamental period, $T_1$. In view of this argument we investigate pair production in an exponentially damped sinusoidal field and find that the initial momenta for multiperiodic trajectories lie on parabolic curves, such that on each curve the ratio $\tilde{T}/T_1$ stays uniform. Evaluation of the tunneling amplitude using these trajectories shows that vacuum decay rate is reduced by an order of magnitude, with respect to the purely time-dependent case, due to the presence of magnetic field.

6 pages, 4 figures. Revised and extended

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Cited by in corpus (13)

• Advances in QED with intense background fields
• Electron-positron pair production in external electric fields varying both in space and time
• Effects of finite spatial extent on Schwinger pair production
• Discrete worldline instantons
• Doubly assisted Sauter-Schwinger effect
• The worldline approach to helicity flip in plane waves
• Worldline instantons for nonlinear Breit-Wheeler pair production and Compton scattering
• WKB approach to pair creation in spacetime-dependent fields
• Quantum tunnelling from vacuum in multidimensions
• Euclidean mirrors: enhanced vacuum decay from reflected instantons
• Hawking Radiation via Complex Geodesics
• Condensed-matter analogs of the Sauter--Schwinger effect
• Pair Production in Real Proper Time and Unitarity Without Borel Ambiguity