  Particles are spontaneously created from the vacuum by time-varying
gravitational or electromagnetic backgrounds. It has been proven that the
particle number operator in an expanding universe is an adiabatic invariant. In
this paper we show that, in some special cases, the expected adiabatic
invariance of the particle number fails in presence of electromagnetic
backgrounds. In order to do this, we consider as a prototype a Sauter-type
electric pulse. Furthermore, we also show a close relation between the breaking
of the adiabatic invariance and the emergence of the axial anomaly.
