Role of switching-on and -off effects in the vacuum instability

Abstract

We find exact differential mean numbers of fermions and bosons created from the vacuum due to a composite electric field of special configuration. This configuration imitates a finite switching-on and -off regime and consists of fields that switch-on exponentially from the infinitely remote past, remains constant during a certain interval T and switch-off exponentially to the infinitely remote future. We show that calculations in the slowly varying field approximation are completely predictable in the framework of a locally constant field approximation.Beyond the slowly varying field approximation, we study effects of fast switching-on and -off in a number of cases when the size of the dimensionless parameter √ eET is either close or exceeds the threshold value that determines the transition from a regime sensitive to on-off parameters to the slowly varying regime for which these effects are secondary.

Violation of vacuum stability by inverse square electric fields

“…2, 3 with 4. These oscillations are consequences of an "abrupt" switching on process near t = 0 and frequently occurs in these cases, as reported recently by us in [23]. In this work, oscillations around the uniform distribution were found and discussed for the case of a T -constant electric field (that switcheson and off "abruptly" at definite time instants) and an electric field composed by independent intervals, one exponentially increasing, another constant over the duration T and a third one exponentially decreasing.…”

“…As an application of the above results, we consider in this section an electric field of special configuration in which inverse square increasing and decreasing electric fields simulate switching on and off processes. This consideration allow us to compare effects with recent results [23], in which a composite electric field of similar form was regarded to study the influence of switching on and off processes in the vacuum.…”

“…Hence, in what follows we present mean numbers N cr n of pairs created from the vacuum by the composite field (51) as a function of the longitudinal momentum p x for some values of the parameters √ eEτ j and √ eET . Moreover, in order to compare switching on and off effects with an another composite electric field [23]…”

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

“…Therefore, it is not unexpected that the mean numbers of pairs created by the composite field N cr n are closer to uniform distribution than the ones created by the L-constant field, provided L is the same for both fields. At last, but not least, it is worth pointing out that features similar to the ones above discussed also occur for time-dependent composite electric fields, as reported by us previously in [24,26].…”

“…In the case of the t-steps, these are particle creation in the constant uniform electric field [14,3], in the adiabatic electric field E (t) = E cosh −2 (t/T S ) [15], in the so-called T -constant electric field [16,17], in a periodic alternating in time electric field [18,19], in an exponentially decaying electric field [20], in an exponentially growing and decaying electric fields [21,22] (see Ref. [23] for the review), in a composite electric field [24], and in an inverse-square electric field (an electric field that is inversely proportional to time squared [26]). In the case of x-steps these are particle creation in the Sauter electric field [13], in the so-called L-constant electric field [25], and in the inhomogeneous exponential peak field [27].…”