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 thinstrip limit. We also investigate the existence of bound states in the nonrelativistic limit and give a geometric quantitative condition for the bound states to exist.
 Publication:

arXiv eprints
 Pub Date:
 January 2021
 arXiv:
 arXiv:2101.04009
 Bibcode:
 2021arXiv210104009B
 Keywords:

 Mathematics  Spectral Theory;
 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Quantum Physics;
 35P05;
 81Q10;
 81Q15;
 81Q37;
 82D77