Shot-noise in transport and beam experiments

Consider two Fermi gases with the same average currents: a transport gas, as in solid-state experiments where the chemical potentials of terminal 1 is mu + eV and of terminal 2 and 3 is mu, and a beam, i.e., electrons entering only from terminal 1 having energies between mu, and mu + eV. By expressing the current noise as a sum over single-particle transitions we show that the temporal current fluctuations are very different: The beam is noisier due to allowed single-particle transitions into empty states below mu. Surprisingly, the correlations between terminals 2 and 3 are the same.