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

Abstract

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.