The conductance of a disordered wire

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Abstract
From an analysis of the scattering theory for a model of a wire with a disordered section, the asymptotic properties of the electrical conductance are derived as the length of the disordered section tends to infinity. It is proved that the conductance decreases exponentially with the length of the disordered section. It is shown that the exponent is two times the smallest Ljapunov exponent associated with a product of random matrices derived from the stationary Schrodinger equation for the system. The distribution of the conductance is asymptotically log-normal. These results are derived from similar properties obtained for the elements of the transmission matrix. The results for the transmission matrix hold equally for the disordered harmonic strip and bar.