Coherent resistance of a disordered 1D wire: Expressions for all moments and evidence for non-Gaussian distribution

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We study coherent electron transport in a one-dimensional wire with disorder modeled as a chain of randomly positioned scatterers. We derive analytical expressions for all statistical moments of the wire resistance ρ. By means of these expressions we show analytically that the distribution P(f) of the variable f=(1+ρ) is not exactly Gaussian even in the limit of weak disorder. In a strict mathematical sense, this conclusion is found to hold not only for the distribution tails but also for the bulk of the distribution P(f).