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Conductance Fluctuations of Disordered Mesoscopic Devices with Many Weakly-Coupled Probes

The conductance coefficients of disordered mesoscopic devices with $n$ probes are investigated within the noninteracting electron approximation at zero temperature. The probes are eliminated from the theoretical description at the expense of introducing nonlocal boundary conditions at the position of the contacts. Conductors with a large number of weak contacts are analyzed in detail. The ensemble-averaged conductance coefficients are in this case given by the so-called Hauser-Feshbach formula $g_{ab} \sim p_a p_b$ where $p_a$ is the probability for emission of an electron into lead $a$. The conductance energy autocorrelation function is shown to deviate significantly from the conventional Lorentzian form and to have a negative tail.