  Spin noise spectroscopy is a promising technique for revealing the
microscopic nature of spin dephasing processes in quantum dots. We compare the
spin-noise in an ensemble of singly charged quantum dots calculated by two
complementary approaches. The Chebyshev polynomial expansion technique (CET)
accounts for the full quantum mechanical fluctuation of the nuclear spin bath
and a semi-classical approach (SCA) is based on the averaging the electron spin
dynamics over all different static Overhauser field configurations.
  We observe a remarkable agreement between both methods in the high-frequency
part of the spectra, while the low-frequency part is determined by the long
time fluctuations of the Overhauser field. We find small differences in the
spectra depending on the distribution of hyperfine couplings. The spin-noise
spectra in strong enough magnetic fields where the nuclear dynamics is quenched
calculated by two complimentary approaches are in perfect agreement.
