Fluctuation of the strength function

We consider a single state stochastically coupled to its stochastic background states. The fluctuation of the strength function of the single state is systematically studied. We find that the upper and lower deviations of the strength function only depend on the ratio of the spreading width over the decay width of the single state and on the ratio of the common decay width over the mean level spacing of the background states. Based on the two fit formulas for the upper and lower deviations, the uncertainties of the full width at half maximum (FWHM) and lifetime of a single state are estimated. They predict the experimental error bars of the FWHM and lifetime. A comparison of the uncertainties with the experimental error bars is made for nuclear giant dipole resonance, which illuminates our theoretical predictions.