Waveguides with asymptotically diverging twisting

TL;DR

This paper introduces a new class of three-dimensional waveguides with diverging twisting angles, demonstrating that their Dirichlet Laplacian spectrum is purely discrete despite the infinite volume.

Contribution

It constructs unbounded waveguides with diverging twist angles where the spectrum remains purely discrete, a novel spectral property for such geometries.

Findings

Spectrum is purely discrete for diverging twist waveguides

Unbounded domains with infinite volume can have discrete spectra

Diverging twisting affects spectral properties significantly

Abstract

We provide a class of unbounded three-dimensional domains of infinite volume for which the spectrum of the associated Dirichlet Laplacian is purely discrete. The construction is based on considering tubes with asymptotically diverging twisting angle.