1111.6014 (Matías Zilly et al.)

Decoherence-induced conductivity in the discrete 1D Anderson model: A
novel approach to even-order generalized Lyapunov exponents    [PDF]

Matías Zilly, Orsolya Ujsághy, Marko Woelki, Dietrich E. Wolf

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.

View original: http://arxiv.org/abs/1111.6014