Decoherence-induced conductivity in the discrete one-dimensional Anderson model: A novel approach to even-order generalized Lyapunov exponents

In: Physical Review / B, Condensed matter and materials physics, Jg. 85 (2012) ; Nr. 7, S. 075110-1 - 075110-11
ISSN: 1098-0121, 0163-1829, 0556-2805
Zeitschriftenaufsatz / Fach: Physik
Fakultät für Physik » Theoretische Physik
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.