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Using a modification of the Shapiro approach, we introduce the two-parameter family of conductance distributions W(g), defined by simple differential equations, which are in the one-to-one correspondence with conductance distributions for quasi-one-dimensional systems of size L^{d-1}\times L_z, characterizing by parameters L/\xi and L_z/L (\xi is the correlation length, d is the dimension of space). This family contains the Gaussian and log-normal distributions, typical for the metallic and localized phases. For a certain choice of parameters, we reproduce the results for the cumulants of conductance in the space dimension d=2+\epsilon obtained in the framework of the \sigma-model approach. The universal property of distributions is existence of two asymptotic regimes, log-normal for small g and exponential for large g. In the metallic phase they refer to remote tails, in the critical region they determine practically all distribution, in the localized phase the former asymptotics forces out the latter. A singularity at g=1, discovered in numerical experiments, is admissible in the framework of their calculational scheme, but related with a deficient definition of conductance. Apar

Author

Suslov, I. M.

Published

2016

Language

EN