Non-adiabatic Quantum Vlasov Equation for Schwinger Pair Production

Abstract

Using Lewis-Riesenfeld theory, we derive an exact non-adiabatic master equation describing the time evolution of the QED Schwinger pair production rate for a general time-varying electric field. This equation can be written equivalently as a first-order matrix equation, as a Vlasov type integral equation, or as a third-order differential equation. In the last version it relates to the KdV equation, which allows us to construct an exact solution using the well-known one-soliton solution to that equation. The case of time-like delta function pulse fields is also shortly considered. We compare with previous approaches to the purely time-dependent field case.

5 pages, final published version, minor modifications

References in corpus (6)

• Worldline Instantons II: The Fluctuation Prefactor
• The Stokes Phenomenon and Schwinger Vacuum Pair Production in Time-Dependent Laser Pulses
• Interference Effects in Schwinger Vacuum Pair Production for Time-Dependent Laser Pulses
• Improved Approximations for Fermion Pair Production in Inhomogeneous Electric Fields
• Ramsey Fringes and Time-domain Multiple-Slit Interference from Vacuum
• Pair Production Beyond the Schwinger Formula in Time-Dependent Electric Fields

Cited by in corpus (27)

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• Lorentzian worldline path integral approach to Schwinger effect
• On the Vlasov equation for Schwinger pair production in a time-dependent electric field
• WKB approach to pair creation in spacetime-dependent fields
• The inverse problem for Schwinger pair production
• Stokes phenomenon and Hawking Radiation
• Unexciting non-Abelian electric fields
• Quantum tunnelling from vacuum in multidimensions
• Generalized quantum Vlasov equation for particle creation and unitary dynamics
• Schwinger Pair Production in Solitonic Gauge Fields
• Second Quantized Scalar QED in Homogeneous Time-Dependent Electromagnetic Fields
• Construction of non-Abelian electric strings
• Quantum kinetic approach to the Schwinger production of scalar particles in an expanding universe
• Quantum Dynamics for de Sitter Radiation
• From nothing to something: discrete integrable systems
• Transient and pre-transient stages in field induced phase transition of vacuum state
• Nonadiabatic quantum Vlasov equation in spinor QED
• Generalized Gelfand-Dikii equation for fermionic Schwinger pair production
• Unexciting classical backgrounds
• Schwinger Pair Production in Pulsed Electric Fields
• Electron-Positron Pair Production in Structured Pulses of Electric Fields
• The physics of adiabatic particle number in the Schwinger effect
• Nonadiabatic quantum kinetic equations and Dirac-Heisenberg-Wigner formalism for Schwinger pair production in time-varying electric fields with multiple components
• When does the Schwinger Preheating Occur?
• Shortcuts to adiabaticity, unexciting backgrounds, and reflectionless potentials