Spectral properties of relativistic quantum waveguides

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.

arXiv commentSome technical results have been moved to the Appendix. To appear on Ann. Henri Poincaré

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Cited by in corpus (4)

• Spectral optimisation of Dirac rectangles
• Spectral inequality for Dirac right triangles
• Dirac operator spectrum in tubes and layers with a zigzag type boundary
• On two-dimensional Dirac operators with critical delta-shell interactions