Noise as a diagnostic of tunneling mechanisms

For three tunneling systems, the classical Coulomb blockade, tunneling of noninteracting particles, and resonant tunneling through an Anderson impurity, the zero frequency current noise provides useful information about the tunneling rates and interactions that is not available by measuring the average current alone. In the case of the Coulomb blockade the noise measures the variance in the number of electrons on the metal particle, while the current measures the mean number of electrons. For tunneling in noninteracting systems the noise measures the mean square variation in energy of the transmission probability as well as the average transmission probability measured by the current. Finally, for resonant tunneling through an Anderson impurity we can show formally that the noise contains information about the mean square variation in the impurity density states as a function of energy. The average current is proportional to the net impurity density of states between the chemical potentials of the two leads.