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

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 $\rho$. By means of these expressions we show analytically that the distribution $P(f)$ of the variable $f=\ln(1+\rho)$ 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 $P(f)$.