Zero Energy Anomaly in One-Dimensional Anderson Lattice with Exponentially Correlated Weak Diagonal Disorder

We calculated numerically the localization length of one-dimensional Anderson model with correlated diagonal disorder. For zero energy point in the weak disorder limit, we showed that the localization length changes continuously as the correlation of the disorder increases. We found that higher order terms of the correlation must be included into the current perturbation result in order to give the correct localization length, and to connect smoothly the anomaly at zero correlation with the perturbation result for large correlation.     

Parametrization of Transfer Matrix： for One-Dimensional Anderson Model with Diagonal Disorder

In this paper, we developed a new parametrization method to calculate the localization length in onedimensional Anderson model with diagonal disorder. This method can avoid the divergence difficulty encountered in the conventional methods, and significantly save computing time as well.     

Unified Description on Behavior of Lyapunov Exponent for 1-D Anderson Model Near Band Center

We investigate the behavior for the Lyapunov exponent around the band center in one-dimensional Anderson model with weak disorder. Using a parametrization method we derive the corresponding differential equation and solve the associated invariant distribution. We obtain the coe?cient for the leading correction term for small energy in band center anomaly. A high precision Pade′ approximation formula is applied to fully amend the anomalous behavior of Lyapunov exponent near band center.