Spectral Properties of Relativistic Quantum Waveguides

William Borrelli, Philippe Briet, David Krejčiřík, Thomas Ourmières-Bonafos

Risultato della ricerca: Contributo in rivistaArticolo in rivistapeer review

Abstract

We make a spectral analysis of the massive Dirac operator in a tubular neighbourhood 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.
Lingua originaleEnglish
pagine (da-a)N/A-N/A
RivistaANNALES HENRI POINCARE'
Volume2022
DOI
Stato di pubblicazionePubblicato - 2022

Keywords

  • Dirac operator
  • infinite mass boundary conditions
  • non-relativistic limit
  • norm-resolvent convergence
  • quantum waveguides
  • thin-waveguide limit

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