Physics – Condensed Matter – Disordered Systems and Neural Networks
Scientific paper
2002-06-20
J. Phys. A: Math. Gen. Vol. 35, pp. 9885-9600 (2002)
Physics
Condensed Matter
Disordered Systems and Neural Networks
33 pages, 6 figures, LaTeX file
Scientific paper
10.1088/0305-4470/35/45/307
We study the nature of electronic states in one-dimensional continuous models with weak correlated disorder. Using a perturbative approach, we compute the inverse localisation length (Lyapunov exponent) up to terms proportional to the fourth power of the potential; this makes possible to analyse the delocalisation transition which takes place when the disorder exhibits specific long-range correlations. We find that the transition consists in a change of the Lyapunov exponent, which switches from a quadratic to a quartic dependence on the strength of the disorder. Within the framework of the fourth-order approximation, we also discuss the different localisation properties which distinguish Gaussian from non-Gaussian random potentials.
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