Spectral properties of relativistic quantum waveguides

• URL: http://arxiv.org/abs/2101.04009v3
• Date: Thu, 10 Mar 2022 17:24:46 GMT
• Title: Spectral properties of relativistic quantum waveguides
• Authors: William Borrelli, Philippe Briet, David Krejcirik, Thomas Ourmieres-Bonafos
• Abstract summary: We find 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 condition for the bound states to exist.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 states to exist.

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