# Spectral Properties of Relativistic Quantum Waveguides

```@article{Borrelli2022SpectralPO,
title={Spectral Properties of Relativistic Quantum Waveguides},
author={William Borrelli and Philippe Briet and David Krej{\vc}iř{\'i}k and Thomas Ourmi{\`e}res-Bonafos},
journal={Annales Henri Poincar{\'e}},
year={2022}
}```
• Published 11 January 2021
• Physics, Mathematics
• Annales Henri Poincaré
We make a spectral analysis of the massive Dirac operator in a tubular neighborhood of an unbounded planar curve, subject to infinite mass boundary conditions. Under general assumptions on the curvature, we locate the essential spectrum and derive an effective Hamiltonian on the base curve which approximates the original operator in the thin-strip limit. We also investigate the existence of bound states in the non-relativistic limit and give a geometric quantitative condition for the bound…
2 Citations
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• 2022
. We consider the two-dimensional Dirac operator with inﬁnite mass boundary condi- tions posed in a tubular neighborhood of a C 4 -planar curve. Under generic assumptions on its curvature κ , we
Dirac operator spectrum in tubes and layers with a zigzag type boundary
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• 2021
We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in R and R of tube or layer shapes with a zigzag type boundary using the corresponding properties of the

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