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Conductance distribution at criticality: one‐dimensional Anderson model with random long‐range hopping
Author(s) -
Méndez A.,
Gopar V.,
Varga I.
Publication year - 2009
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200910390
Subject(s) - anderson localization , condensed matter physics , physics , transmission (telecommunications) , dielectric , conductance , range (aeronautics) , distribution (mathematics) , semiconductor , superlattice , fabry–pérot interferometer , computational physics , materials science , quantum mechanics , mathematical analysis , wavelength , mathematics , telecommunications , computer science , composite material
Abstract We study numerically the conductance distribution function w(T) for the one‐dimensional Anderson model with random long‐range hopping described by the Power‐law Banded Random Matrix model at criticality. We concentrate on the case of two single‐channel leads attached to the system. We observe a smooth transition from localized to delocalized behavior in the conductance distribution by increasing b, the effective bandwidth of the model. Also, for b < 1 we show that w(ln T/T typ ) is scale invariant, where T typ = exp 〈 ln T 〉 is the typical value of T. Moreover, we find that for T < T typ , w(ln T/T typ ) shows a universal behavior proportional to (T/T typ ) ‐1/2 .