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Symmetry, dimension and the distribution of the conductance at the mobility edge

Marc Ruhlander·Peter Markos·C. M. Soukoulis
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Abstract

The probability distribution of the conductance at the mobility edge, $p_c(g)$, in different universality classes and dimensions is investigated numerically for a variety of random systems. It is shown that $p_c(g)$ is universal for systems of given symmetry, dimensionality, and boundary conditions. An analytical form of $p_c(g)$ for small values of $g$ is discussed and agreement with numerical data is observed. For $g > 1$, $\ln p_c(g)$ is proportional to $(g-1)$ rather than $(g-1)^2$.

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Marc Ruhlander, Peter Markos, C. M. Soukoulis. 2001-04-20. Symmetry, dimension and the distribution of the conductance at the mobility edge. https://doi.org/10.1103/physrevb.64.212202

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