Scaling properties of one-dimensional Anderson models in an electric field: Exponential versus factorial localization

We investigate the scaling properties of eigenstates of a one-dimensional Anderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite systems this transition can be described by a simple scaling law based on a single parameter lambda(infinity) = l(infinity)/l(el), the ratio between the Anderson localization length l(el) and the Stark localization length l(el). For finite samples, however, the system size N enters the problem as a third parameter. In that case the global structure of eigenstates is uniquely determined by two scaling parameters lambda(N) = l(infinity)/N and lambda(infinity) = l infinity/l(el).