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 A nderson model in the presence of a constant electric field. The states show a transition from exponential to factorial localization. For infinite syst ems this transition can be described by a simple scaling law based on a sin gle parameter lambda(infinity) = l(infinity)/l(el), the ratio between the A nderson localization length l(el) and the Stark localization length l(el). For finite samples, however, the system size N enters the problem as a thir d parameter. In that case the global structure of eigenstates is uniquely d etermined by two scaling parameters lambda(N) = l(infinity)/N and lambda(in finity) = l infinity/l(el).