Motional broadening in ensembles with heavy-tail frequency distribution

We show that the spectrum of an ensemble of two-level systems can be broadened through "resetting" discrete fluctuations, in contrast to the well-known motional-narrowing effect. The broadening occurs if the ensemble frequency distribution has heavy tails with a diverging first moment. The asymptotic motional broadened line shape is then a Lorentzian. In case there is a physical upper cutoff in the frequency distribution, the broadening effect may still be observed, though only up to a certain fluctuation rate.