Resistance fluctuations, phase randomness and noise in one-dimensional conductors with a long-range correlated potential

When the size (L) of a one-dimensional metallic conductor is less than the correlation length λ−1 of the Gaussian random potential, one expects transport properties to show ballistic behaviour. Using an invariant imbedding method, we study the exact distribution of the resistance, of the phase θ of the reflection amplitude of an incident electron of wave number k0, and of dθ/dk0, for λL<< 1. The resistance is non-self-averaging and the n-th resistance moment varies periodically as (1 − cos 2k0L)n. The charge fluctuation noise, determined by the distribution of dθ/dk0, is constant at low frequencies