Vacuum instability in a constant inhomogeneous electric field. A new example of exact nonperturbative calculations

Abstract

Basic quantum processes (such as particle creation, reflection, and transmission on the corresponding Klein steps) caused by inverse-square electric fields are calculated. These results represent a new example of exact nonperturbative calculations in the framework of QED. The inverse-square electric field is time-independent, inhomogeneous in the $x$-direction, and is inversely proportional to $x$ squared. We find exact solutions of the Dirac and Klein-Gordon equations with such a field and construct corresponding in- and out-states. With the help of these states and using the techniques developed in the framework of QED with $x$-electric potential steps, we calculate characteristics of the vacuum instability, such as differential and total mean numbers of particles created from the vacuum and vacuum-to-vacuum transition probabilities. We study the vacuum instability for two particular backgrounds: for fields widely stretches over the $x$-axis (small-gradient configuration) and for the fields sharply concentrates near the origin $x=0$ (sharp-gradient configuration). We compare exact results with ones calculated numerically. Finally, we consider the electric field configuration, composed by inverse-square fields and by an $x$-independent electric field between them to study the role of growing and decaying processes in the vacuum instability.

arXiv comment50 pages, 10 figures. Typos corrected throughout the text. New results concerning the calculation of total quantities for sharp-gradient fields were added to Sec. 3.2. Refs added

References in corpus (15)

• Electron-positron pairs in physics and astrophysics: from heavy nuclei to black holes
• Vacuum instability in external fields
• Schwinger mechanism revisited
• Density matrix of a quantum field in a particle-creating background
• Quantization of charged fields in the presence of critical potential steps
• Critical Schwinger pair production
• Exactly solvable cases in QED with t-electric potential steps
• Scattering and pair creation by a constant electric field between two capacitor plates
• Particle creation from the vacuum by an exponentially decreasing electric field
• Particle creation by peak electric field
• Pair production from the vacuum by a weakly inhomogeneous space-dependent electric potential step
• Particle scattering and vacuum instability by exponential steps
• Role of switching-on and -off effects in the vacuum instability
• Regularization, renormalization and consistency conditions in QED with x-electric potential steps
• Violation of vacuum stability by inverse square electric fields

Cited by in corpus (5)

• Advances in QED with intense background fields
• Vacuum instability due to the creation of neutral Fermion with anomalous magnetic moment by magnetic-field inhomogeneities
• Schwinger mechanism of magnon-antimagnon pair production on magnetic field inhomogeneities and the bosonic Klein effect
• Calculations of vacuum mean values of spinor field current and energy-momentum tensor in a constant electric background
• Vacuum instability in QED with an asymmetric x-step. New example of exactly solvable case