Rigorous perturbation theory versus variational methods in the spectral study of carbon nanotubes

TL;DR

This paper compares rigorous perturbation theory and variational methods for analyzing the spectral properties of carbon nanotubes, demonstrating strong agreement at small radii based on recent experimental data.

Contribution

It provides a detailed comparison between two analytical approaches for nanotube spectra, highlighting their accuracy and applicability at small radii.

Findings

Excellent agreement between methods at small radii

Perturbation theory is validated against variational results

Analytic approximations match experimental data closely

Abstract

Recent two-photon photo-luminescence experiments give accurate data for the ground and first excited excitonic energies at different nanotube radii. In this paper we compare the analytic approximations proved in \cite{CDR}, with a standard variational approach. We show an excellent agreement at sufficiently small radii.