Conductance distribution at criticality: one‐dimensional Anderson model with random long‐range hopping

作者: A. Méndez , V. Gopar , I. Varga

DOI: 10.1002/ANDP.200910390

关键词:

摘要: We study numerically the conductance distribution function w(T) for one-dimensional Anderson model with random long-range hopping described by Power-law Banded Random Matrix at criticality. concentrate on case of two single-channel leads attached to system. observe a smooth transition from localized delocalized behavior in increasing b, effective bandwidth model. Also, b < 1 we show that w(ln T/Ttyp) is scale invariant, where Ttyp = exp 〈 ln T 〉 typical value T. Moreover, find Ttyp, shows universal proportional (T/Ttyp)-1/2.

参考文章(22)
J. A. Méndez-Bermúdez, I. Varga, Scattering at the Anderson transition : Power-law banded random matrix model Physical Review B. ,vol. 74, pp. 125114- ,(2006) , 10.1103/PHYSREVB.74.125114
Imre Varga, Daniel Braun, Critical statistics in a power-law random-banded matrix ensemble Physical Review B. ,vol. 61, ,(2000) , 10.1103/PHYSREVB.61.R11859
L. Schweitzer, P. Markoš, Universal Conductance and Conductivity at Critical Points in Integer Quantum Hall Systems Physical Review Letters. ,vol. 95, pp. 256805- ,(2005) , 10.1103/PHYSREVLETT.95.256805
Alexander D. Mirlin, Yan V. Fyodorov, Frank-Michael Dittes, Javier Quezada, Thomas H. Seligman, Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices Physical Review E. ,vol. 54, pp. 3221- 3230 ,(1996) , 10.1103/PHYSREVE.54.3221
Cécile Monthus, Thomas Garel, Statistics of the two-point transmission at Anderson localization transitions Physical Review B. ,vol. 79, pp. 205120- ,(2009) , 10.1103/PHYSREVB.79.205120
J.J.M. Verbaarschot, H.A. Weidenmüller, M.R. Zirnbauer, Grassmann integration in stochastic quantum physics: The case of compound-nucleus scattering Physics Reports. ,vol. 129, pp. 367- 438 ,(1985) , 10.1016/0370-1573(85)90070-5