M. Weiss et al., Scaling properties of one-dimensional Anderson models in an electric field: Exponential versus factorial localization, PHYS REV B, 62(3), 2000, pp. 1765-1772
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).