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For chaotic cavities with scattering leads attached, transport properties can be approximated in terms of the classical trajectories which enter and exit the system. With a semiclassical treatment involving fine correlations between such trajectories we develop a diagrammatic technique to calculate the moments of various transport quantities. Namely, we find the moments of the transmission and reflection eigenvalues for systems with and without time reversal symmetry. We also derive relateddoi:10.1088/1367-2630/13/6/063020 fatcat:ofyteucsq5bprfqrk6ovkuhuqa