Short-distance wavefunction statistics in one-dimensional Anderson localization

TL;DR

This paper explores how short-distance local density of states statistics in 1D Anderson localized systems can be derived from long-distance wavefunction data, revealing new insights beyond traditional scaling theory.

Contribution

It demonstrates that the distribution of local density of states can be reconstructed from long-distance wavefunction statistics using additional parameters outside the standard two-parameter scaling framework.

Findings

P(nu) can be obtained from wavefunction statistics

Short-distance density of states is linked to long-distance behavior

Additional parameters are needed beyond two-parameter scaling

Abstract

We investigate the short-distance statistics of the local density of states nu in long one-dimensional disordered systems, which display Anderson localization. It is shown that the probability distribution function P(nu) can be recovered from the long-distance wavefunction statistics, if one also uses parameters that are irrelevant from the perspective of two-parameter scaling theory.