Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory

Abstract

The non-perturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields $\vec{E}(\vec{x},t)$. Based on the Dirac-Heisenberg-Wigner (DHW), formalism we derive a system of partial differential equations of infinite order for the sixteen irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory (QKT) is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field $E(t)=E_0$ and the Sauter-type electric field $E(t)=E_0{\mathrm{sech}}^2(t/\tau )$. These analytic solutions translate into corresponding expressions within the DHW formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.

17 pages, 5 figures. Typos corrected and references added, PRD Version

References in corpus (12)

• Dynamically assisted Schwinger mechanism
• Worldline Instantons II: The Fluctuation Prefactor
• Momentum signatures for Schwinger pair production in short laser pulses with a sub-cycle structure
• The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
• Finite size effects in stimulated laser pair production
• Barrier control in tunneling e^+ e^- photoproduction
• The Schwinger mechanism revisited
• Pair Production Beyond the Schwinger Formula in Time-Dependent Electric Fields
• Multidimensional Worldline Instantons
• Gutzwiller's Trace Formula and Vacuum Pair Production
• Vacuum Persistence and Inversion of Spin Statistics in Strong QED
• Semiclassical Treatment of Induced Schwinger Processes at Finite Temperature

Cited by in corpus (4)

• Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses
• Strong field effects in laser pulses: the Wigner formalism
• Schwinger effect in inhomogeneous electric fields
• Time evolution of the QED vacuum in a uniform electric Field: Complete analytic solution by spinorial decomposition