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

Abstract

We investigate the scaling properties of eigenstates of a one-dimensional (1D) 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 ${\lambda }_{\infty }=l_{\infty }/l_{\mathrm{el}}$, the ratio between the Anderson localization length $l_{\infty }$ and the Stark localization length~$l_{\mathrm{el}}$. 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 ${\lambda }_N=l_{\infty }/N$ and ${\lambda }_{\infty }=l_{\infty }/l_{\mathrm{el}}$.

9 pages, 8 figures, Phys. Rev. B, to appear

References in corpus (1)

• The spatial statistical properties of wave functions in a disordered finite one-dimensional sample