Three types of spectra in one-dimensional systems with random correlated binary potential

TL;DR

This paper introduces a method to generate one-dimensional binary potentials with long-range correlations, resulting in a hybrid spectrum comprising absolutely continuous, singular continuous, and point spectra, analyzed through a novel additive Markov chain approach.

Contribution

The paper presents a new algorithm for constructing correlated binary potentials with a predefined spectral composition in one-dimensional systems.

Findings

Successfully generates binary potentials with three spectral types

Demonstrates control over spectral ordering in energy/wave number

Uses additive Markov chains for long-range correlation modeling

Abstract

The stationary one-dimensional tight-binding Schredinger equation with a weak diagonal long-range correlated disorder in the potential is studied. An algorithm for constructing the discrete binary on-site potential exhibiting a hybrid spectrum with three different spectral components (absolutely continuous, singular continuous and point) ordered in any predefined manner in the region of energy and/or wave number is presented. A new approach to generating a binary sequence with the long-range memory based on a concept of additive Markov chains (Phys. Rev. E 68, 061107 (2003)) is used.