  A new exactly solvable case in strong-field quantum electrodynamics with a
time-dependent external electric field is presented. The corresponding field is
given by an analytic function, which is asymmetric (in contrast to Sauter-like
electric field) with respect to the time instant, where it reaches its maximum
value, that is why we call it the analytic asymmetric electric field. We
managed to exactly solve the Dirac equation with such a field, which made it
possible to calculate characteristics of the corresponding vacuum instability
nonperturbatively. We construct the so-called in- and out-solutions and with
their help calculate mean differential and total numbers of created charged
particles, probability of the vacuum to remain a vacuum, vacuum mean values of
current density and energy-momentum tensor of the particles. We study the
vacuum instability in regimes of rapidly and slowly changing analytic
asymmetric electric field, and compare the obtained results with corresponding
ones obtained earlier for the case of the symmetric Sauter-like electric field.
We also compare exact results in the regime of slowly changing field with
corresponding results obtained within the slowly varying field approximation
recently proposed by two of the authors, thus demonstrating the effectiveness
of such an approximation.
