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When a system is thermally coupled to only a small part of a larger bath,statistical fluctuations of the temperature (more precisely, the internalenergy) of this "sub-bath" around the mean temperature defined by the largerbath can become significant. We show that these temperature fluctuationsgenerally give rise to 1/f-like noise power spectral density from even a singletwo-level system. We extend these results to a distribution of fluctuators,finding the corresponding modification to the Dutta-Horn relation. Then weconsider the specific situation of charge noise in silicon quantum dot qubitsand show that recent experimental data [E. J. Connors, et al., Phys. Rev. B100, 165305 (2019)] can be modeled as arising from as few as two two-levelfluctuators, and accounting for sub-bath size improves the quality of the fit.

Microscopic bath effects on noise spectra in semiconductor quantum dot qubits