Inverse localization length for the one-dimensional Anderson model for small disorder

A transfer operator method is used to calculate the inverse localization length, $\alpha$, of the one-dimensional Anderson model as a function of disorder, $\sigma$. For small disorder $\alpha$ vanishes as $\alpha =A{\sigma }^2+O\left({\sigma }^4\right)$, with $A=0.2088\mathrm{}$.