Simple model for a Quantum Wire II. Correlations

TL;DR

This paper extends a simple quantum wire model by incorporating correlations among sites, revealing how correlated disorder affects state distribution and electron localization.

Contribution

It introduces a method to include correlations in the model, advancing understanding of disorder effects in quantum wires.

Findings

Correlated disorder alters the distribution of states.

Correlations influence electron localization.

The model provides analytical insights into correlated systems.

Abstract

In a previous paper (Eur. Phys. J. B 30, 239-251 (2002)) we have presented the main features and properties of a simple model which -in spite of its simplicity- describes quite accurately the qualitative behaviour of a quantum wire. The model was composed of N distinct deltas each one carrying a different coupling. We were able to diagonalize the Hamiltonian in the periodic case and yield a complete and analytic description of the subsequent band structure. Furthermore the random case was also analyzed and we were able to describe Anderson localization and fractal structure of the conductance. In the present paper we go one step further and show how to introduce correlations among the sites of the wire. The presence of a correlated disorder manifests itself by altering the distribution of states and the localization of the electrons within the system