Decoherence-induced conductivity in the discrete 1D Anderson model: A   novel approach to even-order generalized Lyapunov exponents
  A recently proposed statistical model for the effects of decoherence on electron transport manifests a decoherence-driven transition from quantum-coherent localized to ohmic behavior when applied to the one-dimensional Anderson model. Here we derive the resistivity in the ohmic case and show that the transition to localized behavior occurs when the coherence length surpasses a value which only depends on the second-order generalized Lyapunov exponent $\xi^{-1}$. We determine the exact value of $\xi^{-1}$ of an infinite system for arbitrary uncorrelated disorder and electron energy. Likewise all higher even-order generalized Lyapunov exponents can be calculated, as exemplified for fourth order. An approximation for the localization length (inverse standard Lyapunov exponent) is presented, by assuming a log-normal limiting distribution for the dimensionless conductance $T$. This approximation works well in the limit of weak disorder, with the exception of the band edges and the band center. 
Mat\'ias Zilly and Orsolya Ujs\'aghy and Marko Woelki and Dietrich E.   Wolf
cond-mat.mes-hall