Calculus of Variations and Geometric Measure Theory
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W. Borrelli - P. Briet - D. Krejcirik - T. Ourmieres-Bonafos

Spectral properties of relativistic quantum waveguides

created by borrelli on 13 Jan 2021


Submitted Paper

Inserted: 13 jan 2021

Year: 2021

ArXiv: 2101.04009 PDF


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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