Information Length and Localization in One Dimension

TL;DR

This paper investigates the scaling properties of wave functions in the one-dimensional Anderson model using a novel entropic length measure, showing strong agreement with analytical predictions across various disorder levels.

Contribution

Introduces a new entropic length measure for wave functions and validates it against analytical results in finite one-dimensional Anderson systems.

Findings

Entropic length agrees with analytical models for systems of 10^3 to 10^4 sites.

The method is effective over a wide range of disorder parameters.

Implications for higher-dimensional systems are discussed.

Abstract

The scaling properties of the wave functions in finite samples of the one dimensional Anderson model are analyzed. The states have been characterized using a new form of the information or entropic length, and compared with analytical results obtained by assuming an exponential envelope function. A perfect agreement is obtained already for systems of $10^3$--$10^4$ sites over a very wide range of disorder parameter $10^{-4}<W<10^4$. Implications for higher dimensions are also presented.