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.

Vacuum instability due to the creation of neutral fermion with anomalous magnetic moment by magnetic-field inhomogeneities

“…More precisely, it was found a few years ago [87,88] that the imaginary part of the effective action of QED (both scalar as spinor) scales with 1 − γ 2 in a universal way, irrespective of the asymptotic behavior of the electric field. Recently [77], we arrived at the same conclusion studying the problem for an specific electric field and discovered that this compatibility results from the universal behavior of mean numbers when the Klein zone is small. Inspired by the close analogy with pure QED and according to peculiarities of differential mean numbers for sharply varying magnetic steps, we have reasons to believe the differential mean number of pairs created from the vacuum behaves universally as eq.…”

“…Recently [77], we have demonstrated for the inverse-square electric field that this peculiarity also follows from the behavior of total quantities when the Klein zone is relatively small. Because of the condition (4.12), not only the parameter U/2 is small but all parameters involving the quantum numbers p x , p z , and ω are small as well on account of the inequalities (3.2).…”

“…in refs. [77][78][79][80][81]. In our subsequent calculations, we rely on a modification of the general theory described in refs.…”

“…(2.12) with the number of step potentials, namely, the Sauter potential, A 0 (y) = −E tanh (y/ ), [4], step between two capacitor plates, and configurations of two exponential steps or two inverse potential steps; see refs. [77][78][79][80][81]. We consider the following external field…”

Radiation Problems Accompanying Carrier Production by an Electric Field in the Graphene

“…[24] for the review), in a composite electric field [25], and in an inverse-square electric field [26]. In the case of x-steps, these are particle creation in the Sauter electric field [17], in the so-called L-constant electric field [27], and in the inhomogeneous exponential peak field [28] and inverse-square electric field [26,29].…”