Abstract
AbstractResistance fluctuations in the presence of an applied voltage are studied, using the Riccati equation for the reflection coefficient of a random conductor obtained by an invariant imbedding approach. As in the previously studied zero‐field case the conductor of length L is described by a Gaussian barrier, V(L), with a systematic part V, and the analysis is restricted to incident kinetic energies of the order of typical values of V(L)/2. The reflection coefficient is related to a resistance variable ϱ via the Landauer formula. Expressions for the distribution of the Landauer resistance and for its low order moments are obtained for arbitrary voltages and lengths L. The distribution of ϱ is exponential for L → 0 and log‐normal for L → ∞, with exponentially increasing mean‐ and rms‐values. The variable ln ϱ is self‐averaging at sufficiently low voltage. The properties of the reflection coefficient are discussed exactly in a different energy range, namely for low incident kinetic energies.
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