Decoherence-induced conductivity in the discrete one-dimensional 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 ξ−1. We determine the exact value of ξ−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.
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