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The low-frequency current-fluctuation spectra of phase-coherent electron conductors are related to the scattering matrix of the conductor. Each contact of the conductor is connected to a thermal equilibrium electron reservoir. The current-current correlations of the conductor are compared with the intensity-intensity correlations of a photon wave guide with all its ports connected to blackbody radiation sources. Only two sources of noise are considered: (a) Fluctuations in the occupation numbers of the incident channels that reflect the thermal equilibrium fluctuations of the reservoir states and (b) a shot noise (or partition noise) that originates if a carrier can be scattered into more than one final state and is present even at zero temperature. The theory uses single-particle scattering states to build up multiparticle states with the proper symmetry. Second quantization provides an elegant treatment of this problem if annihilation and creation operators for both the input and output channels of the wave guide are introduced. At equilibrium, in the absence of transport, the correlations of flux fluctuations measured at two different contacts are negative for both fermions and bosons. Away from equilibrium, in the presence of a net flux, the fluctuations are related to transport coefficients which invoke products of four scattering matrices.The transport portion of the correlation of the flux fluctuations at two different contacts is negative for fermions but is positive for bosons. The transport portion (shot noise) is very sensitive to the transmission behavior of the wave guide. Both for fermions and for bosons completely open transmission channels give no contribution. In addition to two-terminal conductors, we consider four-probe conductors in high magnetic fields which have the property that carriers transmitted and reflected at a barrier reach separate contacts. We discuss a four-terminal experiment which explicitly shows that the correlation function in the presence of two particle sources is not an incoherent sum of correlations generated by particles originating in one of the sources but contains exchange terms due to the indistinguishability of identical particles. We discuss the conditions for such exchange terms to be sensitive to a quantum-mechanical phase and the possibility to tune this phase with the help of an Aharonov-Bohm flux.
Μ. Büttiker (Sun,) studied this question.