From closed to open 1D Anderson model: Transport versus spectral statistics

TL;DR

This paper establishes a linear relationship between spectral statistics parameter and localization length in the 1D Anderson model, enabling comprehensive description of transport properties across localized and extended regimes.

Contribution

It introduces a universal relation linking spectral statistics parameter to localization length, unifying transport descriptions in the 1D Anderson model across different regimes.

Findings

Linear relation between spectral parameter and localization length.

Transport properties depend solely on spectral parameter and coupling strength.

Unusual interplay observed between internal chaos and openness.

Abstract

Using the phenomenological expression for the level spacing distribution with only one parameter, $0 \leq \beta \leq \infty$, covering all regimes of chaos and complexity in a quantum system, we show that transport properties of the one-dimensional Anderson model of finite size can be expressed in terms of this parameter. Specifically, we demonstrate a strictly linear relation between $\beta$ and the normalized localization length for the whole transition from strongly localized to extended states. This result allows one to describe all transport properties in the open system entirely in terms of the parameter $\beta$ and strength of coupling to continuum. For non-perfect coupling, our data show a quite unusual interplay between the degree of internal chaos defined by $\beta$, and degree of openness of the model. The results can be experimentally tested in single-mode waveguides with either bulk or surface disorder.