Random-matrix study of multiprobe mesoscopic devices: A three-probe one-dimensional system

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Abstract
A random-matrix analysis is presented for the simplest multiprobe system, a three-terminal device consisting of one-dimensional wires, that allows the study of the voltage drop along a disordered meso- scopic conductor. The calculation of the actual statistical distribution of the measured voltage is reduced to quadratures. This distribution is, in general, so wide that the voltage measured at the midpoint of a strongly disordered conductor of a given length falls, with appreciable probability, in the vicinity of the voltage of either terminal. Under these circumstances the measured voltage cannot be regarded as a macroscopic variable in the usual sense. One consequence of so wide a distribution is that in a four-terminal arrangement one may measure with nonzero probability an uphill voltage. A very wide distribution is also obtained when the conductor in question is a perfect one and an ensemble of splitters that couple the conductor to the measuring probe is considered. Striking nonlocal effects of a quantum-mechanical origin are also explicitly demonstrated.