Shot-noise in transport and beam experiments

Consider two Fermi gases with the same {\it 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.