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Two independent measurements of cross sections for the 19F+93Nb dissipative heavy-ion collision (DHIC) have been performed at incident energies from 100 to 108 MeV in steps of 250 keV. Two independently prepared targets were used respectively with all other experimental conditions being identical in both experiments. The data indicate non-reproducibility of the non-self-averaging oscillation yields in the two measurements. The statistical analysis of this non-reproducibility supports recent theoretical predictions of spontaneous coherence, slow phase randomization and extreme sensitivity in highly excited quantum many-body systems.