“One-Sided” Log-Normal Distribution of Conductances for a Disordered Quantum Wire

We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of the conductance $P\left(g\right)$ for a quasi-one-dimensional wire in the absence of electron-electron interactions. We show that in the crossover region between the metallic and insulating regimes $P\left(g\right)$ is highly asymmetric, given by an essentially “one-sided” log-normal distribution. For larger disorder, the tail of the log-normal distribution for $g>\mathrm{}1\mathrm{}$ is cut off by a Gaussian.