Universal distribution functions in two-dimensional localized systems.
We find the conductance distribution function of the two-dimensional Anderson model in the strongly localized limit. The fluctuations of lng grow with lateral size as L1/3 and follow a universal distribution that depends on the type of leads. For narrow leads, it is the Tracy-Widom distribution, which appears in the problem of the largest eigenvalue of random matrices from the Gaussian unitary ensemble and in many other problems like the longest increasing subsequence of a permutation, directed polymers, or polynuclear growth. We also show that for wide leads the conductance follows a related, but different, distribution.
Somoza
A M
AM
Departamento de Física-CIOyN, Universidad de Murcia, Murcia 30.071, Spain.
Ortuño
M
M
Prior
J
J