The power spectrum of quantum dot fluorescence exhibits $1/f^beta$ noise, related to the intermittency of these nanosystems. As in other systems exhibiting $1/f$ noise, this power spectrum is not integrable at low frequencies, which appears to imply infinite total power. We report measurements of individual quantum dots that address this long-standing paradox. We find that the level of $1/f^beta$ noise decays with the observation time. The change of the spectrum with time places a bound on the total power. These observations are in stark contrast with most measurements of noise in macroscopic systems which do not exhibit any evidence for non-stationarity. We show that the traditional description of the power spectrum with a single exponent $beta$ is incomplete and three additional critical exponents characterize the dependence on experimental time.
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