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Owing to effects arising from quantum electrodynamics (QED),magnetohydrodynamical fast modes of sufficient strength will break down to formelectron-positron pairs while traversing the magnetospheres of stronglymagnetised neutron stars. The bulk of the energy of the fast mode fuels thedevelopment of an electron-positron fireball. However, a small, but potentiallyobservable, fraction of the energy ($\sim 10^{33}$ ergs) can generate anon-thermal distribution of electrons and positrons far from the star. Thispaper examines the cooling and radiative output of these particles. Small-scalewaves may produce only the non-thermal emission. The properties of thisnon-thermal emission in the absence of a fireball match those of the quiescent,non-thermal radiation recently observed non-thermal emission from severalanomalous X-ray pulsars and soft-gamma repeaters. Initial estimates of theemission as a function of angle indicate that the non-thermal emission shouldbe beamed and therefore one would expect this emission to be pulsed as well.According to this model the pulsation of the non-thermal emission should bebetween 90 and 180 degrees out of phase from the thermal emission from thestellar surface.Comment: 7 pages, 5 figures, to appear in the proceedings of the conference  "Isolated Neutron Stars: from the Interior to the Surface" (April 2006,  London), eds. D. Page, R. Turolla, & S. Zane, Astrophysics & Space Scienc

QED can explain the non-thermal emission from SGRs and AXPs: variability