Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces

TL;DR

This paper investigates eigenstate structures in quasi-1D waveguides with rough surfaces, revealing many regular eigenstates that cause slow classical convergence and exhibit unusual localization properties, challenging standard statistical models.

Contribution

It provides analytical and numerical evidence of regular eigenstates in high-energy regimes, showing their impact on localization and classical limit convergence in rough waveguides.

Findings

Presence of many regular eigenstates at high energy

Localization properties vary with eigenstate type

Standard statistical models may not apply

Abstract

Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes, are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpeted form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be unappropriate.