Particle creation from the vacuum by an exponentially decreasing electric field

Abstract

We analyze the creation of fermions and bosons from the vacuum by the exponentially decreasing in time electric field in detail. In our calculations we use QED and follow in main the consideration of particle creation effect in a homogeneous electric field. To this end we find complete sets of exact solutions of the d-dimensional Dirac equation in the exponentially decreasing electric field and use them to calculate all the characteristics of the effect, in particular, the total number of created particles and the probability of a vacuum to remain a vacuum. It should be noted that the latter quantities were derived in the case under consideration for the first time. All possible asymptotic regimes are discussed in detail. In addition, switching on and switching off effects are studied.

Particle creation by peak electric field

“…, we can compare the above results with the results of the regularization of rectangular steps by the Sauter-like potential [40], obtained for a small T S → 0 and constant U = 2eE T S under the conditions U T S 1 and max{T S ω 1 , T S ω 2 } 1. We see that both regularizations are in agreement for fermions under the condition |ω 2 − ω 1 | U , and for bosons under the condition (ω 2 − ω 1 )…”

“…The latter property implies that a peak at t = 0 is present. Time-dependent electric fields of this form can, as usual in QED with unstable vacuum [6][7][8][9] (see also [40]), be described by t-electric potential steps,…”

“…As customary for t-electric steps [40], solutions of the Dirac equation (2.5) have the form 6) where ψ n (t) and φ n (t) are spinors which depend on t alone. In fact, these are states with definite momenta p. Substituting Eq.…”

“…[30]. Note that the pair creation due to an exponentially decaying background has been studied in de Sitter spacetime and for the constant electric field in two dimensional de Sitter spacetime; see, e.g., [21,42] and references therein.…”

Electron-positron pair production in external electric fields varying both in space and time

“…For the analytically solvable cases discussed in Refs. [14][15][16][17] our calculations reproduce the exact values with perfect accuracy. It is possible to consider an arbitrary function E(t) and, moreover, this technique can be easily modified in order to treat arbitrary static fields E(x), which are inhomogeneous in one space direction [18,19].…”