We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in R 2 and R 3 of tube or layer shapes with a zigzag-type boundary using the corresponding properties of the Dirichlet Laplacian.

• Klíčová slova
• Dirac operator, Quantum waveguide, Spectral analysis, Zigzag boundary conditions,
• Publikační typ
• časopisecké články MeSH

In this note the two dimensional Dirac operator A η with an electrostatic δ -shell interaction of strength η ∈ R supported on a straight line is studied. We observe a spectral transition in the sense that for the critical interaction strengths η = ± 2 the continuous spectrum of A η inside the spectral gap of the free Dirac operator A 0 collapses abruptly to a single point.

• Klíčová slova
• Boundary triple, Dirac operator, Singular potential, Spectral transition,
• Publikační typ
• časopisecké články MeSH