TY - JOUR

T1 - Vacuum instability in a constant inhomogeneous electric field

T2 - a new example of exact nonperturbative calculations

AU - Adorno, T. C.

AU - Gavrilov, S. P.

AU - Gitman, D. M.

N1 - Publisher Copyright:
© 2020, The Author(s).

PY - 2020/2/1

Y1 - 2020/2/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85078903251&partnerID=8YFLogxK

U2 - 10.1140/epjc/s10052-020-7646-y

DO - 10.1140/epjc/s10052-020-7646-y

M3 - Article

AN - SCOPUS:85078903251

SN - 1434-6044

VL - 80

JO - European Physical Journal C

JF - European Physical Journal C

IS - 2

M1 - 88

ER -