Energy spectra of quasiperiodic systems via information entropy

TL;DR

This paper explores how the energy spectra of one-dimensional quasiperiodic systems, like Fibonacci chains, relate to their configurational order, highlighting the role of information entropy in characterizing their spectral complexity.

Contribution

It introduces the concept that minimized information entropy characterizes quasiperiodic arrangements, linking spectral properties to informational content beyond periodic systems.

Findings

Quasiperiodic systems encode more information than periodic ones.

Information entropy is minimized in quasiperiodic energy spectra.

Results have implications for understanding quasiperiodic order in materials.

Abstract

We study the relationship between the electronic spectrum structure and the configurational order of one-dimensional quasiperiodic systems. We take the Fibonacci case as an specific example, but the ideas outlined here may be useful to accurately describe the energy spectra of general quasiperiodic systems of technological interest. Our main result concerns the {\em minimization} of the information entropy as a characteristic feature associated to quasiperiodic arrangements. This feature is shown to be related to the ability of quasiperiodic systems to encode more information, in the Shannon sense, than periodic ones. In the conclusion we comment on interesting implications of these results on further developments on the issue of quasiperiodic order.