Vacuum instability in QED with an asymmetric x-step. New example of exactly solvable case

Abstract

We present a new exactly solvable case in strong-field QED with one-dimensional step potential (x-step). The corresponding x-step is given by an analytic asymmetric with respect to the axis x reflection function. The step can be considered as a certain analytic "deformation" of the symmetric Sauter field. Moreover, it can be treated as a new regularization of the Klein step field. We study the vacuum instability caused by this x-step in the framework of a nonperturbative approach to strong-field QED. Exact solutions of the Dirac equation used in the corresponding nonperturbative calculations, are represented in the form of stationary plane waves with special left and right asymptotics and identified as components of initial and final wave packets of particles. We show that in spite of the fact that the symmetry with respect to positive and negative bands of energies is broken, distribution of created pairs and other physical quantities can be expressed via elementary functions. We consider the processes of transmission and reflection in the ranges of the stable vacuum and study physical quantities specifying the vacuum instability. We find the differential mean numbers of electron-positron pairs created from the vacuum, the components of current density and energy-momentum tensor of the created electrons and positrons leaving the area of the strong field under consideration. Besides, we study the particular case of the particle creation due to a weakly inhomogeneous electric field and obtain explicitly the total number, the current density and energy-momentum tensor of created particles. Unlike the symmetric case of the Sauter field the asymmetric form of the field under consideration causes the energy density and longitudinal pressure of created electrons to be not equal to the energy density and longitudinal pressure of created positrons.

arXiv comment37 pages

References in corpus (15)

• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Advances in QED with intense background fields
• History and Physics of the Klein Paradox
• Schwinger mechanism revisited
• Strong-Field Physics in QED and QCD: From Fundamentals to Applications
• Quantization of charged fields in the presence of critical potential steps
• Scattering and pair creation by a constant electric field between two capacitor plates
• Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential step
• Particle scattering and vacuum instability by exponential steps
• Creation of neutral fermions with anomalous magnetic moments from a vacuum by inhomogeneous magnetic field
• Regularization, renormalization and consistency conditions in QED with x-electric potential steps
• Vacuum instability in a constant inhomogeneous electric field. A new example of exact nonperturbative calculations
• Schwinger pair creation in Dirac semimetals in the presence of external magnetic and electric fields
• Vacuum instability due to the creation of neutral Fermion with anomalous magnetic moment by magnetic-field inhomogeneities
• Calculations of vacuum mean values of spinor field current and energy-momentum tensor in a constant electric background