Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2003-05-30
Annals of Physics, Volume 308, pages 156-200 (2003)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 figures, 50 pages (figures included). To appear in Annals of Physics
Scientific paper
10.1016/S0003-4916(03)00136-2
We develop a simple systematic method, valid for all strengths of disorder, to obtain analytically the full distribution of conductances P(g) for a quasi one dimensional wire within the model of non-interacting fermions. The method has been used in [1-3] to predict sharp features in P(g) near g=1 and the existence of non-analyticity in the conductance distribution in the insulating and crossover regimes, as well as to show how P(g) changes from Gaussian to log-normal behavior as the disorder strength is increased. Here we provide many details of the method, including intermediate results that offer much insight into the nature of the solutions. In addition, we show within the same framework that while for metals P(g) is a Gaussian around g >>1, there exists a log-normal tail for g << 1, consistent with earlier field theory calculations. We also obtain several other results that compare very well with available exact results in the metallic and insulating regimes.
Gopar Victor A.
Muttalib Khandker A.
Woelfle Peter
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