  We develop a theory of spin noise spectroscopy of itinerant, noninteracting,
spin-carrying fermions in different regimes of temperature and disorder. We use
kinetic equations for the density matrix in spin variables. We find a general
result with a clear physical interpretation, and discuss its dependence on
temperature, the size of the system, and applied magnetic field. We consider
two classes of experimental probes: 1. electron-spin-resonance (ESR)-type
measurements, in which the probe response to a uniform magnetization increases
linearly with the volume sampled, and 2. optical Kerr/Faraday rotation-type
measurements, in which the probe response to a uniform magnetization increases
linearly with the length of the light propagation in the sample, but is
independent of the cross section of the light beam. Our theory provides a
framework for interpreting recent experiments on atomic gases and conduction
electrons in semiconductors and provides a baseline for identifying the effects
of interactions on spin noise spectroscopy.
